Number Theory Integer Types by Michael Carter

Carl Friedrich Gauss was known as one of the top ten greatest mathematicians. He was known as the prince of mathematics. Gauss is quoted calling mathematics the "queen of the sciences" and calling number theory the "queen of mathematics. is called "higher arithmetic." Number Theory is the study of whole numbers and sometimes spills over to rational numbers. The whole numbers that is the most fascinating are the primes. We know very little about the primes. Because we know so little about the primes we can make encryption for banks and computer security systems. We also have another fascinating number that we know more about, the composite numbers. The composite numbers are composed of

There are approximately 10 fields within Number Theory: Elementary, Analytic, Algebraic, Geometry, Combinatorial, Computational, Arithmetic Algebraic, Arithmetic Topology, Arithmetic Dynamics, and Modular Form. All these fields can take advantage of this maple package.

This Maple package is called inttypes, which is short for Integer Types. The inttypes package provides over 160 whole number types for Number Theorists to explore numbers. This package may be used as a tool for an academic course, Maple programming, or for research. It is also fun to play with these types for exploration and developing intuition about numbers. In addition, to these number theory integer types, this package also offers three very important functions: ithcomposite, ithprimorial, and printtypes. Maple have a function called, ithprime; which is used to find a particular prime based on its order. This inttypes package provides a function that gives a particular composite number based on its order, called ithcomposite. There is also an ithprimorial function that provides a particular primordial number based on its order. Finally, we have a function that will search among all the types of this package for a number, 1729, is a good test for printtypes (see below). The number, 3, is also a good test for the printtypes function. On the Number Theory Types Test: Just change the integer on each of the for-loops for larger tests when testing the number theory types.

All types return a Boolean value of either true or false. It does not return a number. Note in the testing of the types below we can give input but the outpus is true or false. The input integer is not the output, hence, do not get confused and begin believing that the input is the output.

Finally, there is an official website for referencing and testing the

http://oeis.org/

I hope you enjoy this package as much as I enjoyed creating it for you. Cheers.

======Application Setup Instructions ======

This package was designed on Maple 15. It may work on earlier versions of Maple, however, you would need to make modifications in the maple.ini file to make this happen.

If you have not done so already, extract all the files from the file inttypes.zip to the "C:\inttypes" folder. These instructions assume that this location is "C:\inttypes" Place the maple.ini file in the "C:\Program Files\Maple 15\Users folder" Maple will automatically find this package when you load it using the "with" statement.

If you do not have permission to place files in the "C:\Program Files\Maple 15\Users" folder then see "Alternate Setup Instructions."

Start Maple. type with(inttypes);

Alternate Setup Instructions ======

If you do not have permission to place files in the "C:\Program Files\Maple 15\Users" folder then To do this inside a worksheet, at the prompt, enter the commands:

intlibname := "C:/inttypes": libname := intlibname, libname: with(inttypes); ======

# Number Theory Type Type's Name ======#1) compositenum "Composite Number" #2) prime "Prime Number" (internal to maple) #3) semiprime "Semiprime"

#4) almostprime3 "3-Almost Prime" #5) almostprime4 "4-Almost Prime" #6) almostprime5 "5-Almost Prime" #7) almostprime6 "6-Almost Prime" #8) almostprime7 "7-Almost Prime" #9) almostprime8 "8-Almost Prime" #10) almostprime9 "9-Almost Prime" #11) almostprime10 "10-Almost Prime" #12) almostprime11 "11-Almost Prime" #13) almostprime12 "12-Almost Prime" #14) almostprime13 "13-Almost Prime" #15) almostprime14 "14-Almost Prime" #16) almostprime15 "15-Almost Prime" #17) almostprime16 "16-Almost Prime" #18) almostprime17 "17-Almost Prime" #19) almostprime18 "18-Almost Prime" #20) almostprime19 "19-Almost Prime" #21) almostprime20 "20-Almost Prime"

#22) perfectnum "Perfect Number" #23) mersennenum "Mersenne Number" #24) mersenneexpprime "Mersenne Exponent Prime" #25) mersenneprime "Mersenne Prime" #26) doublemersenneprime "Double Mersenne Prime" #27) fibonaccinum "Fibonacci Number" #28) fibonacciprime "Fibonacci Prime" #29) permutableprime "Permutable Prime" #30) lessertwinprime "Lesser Twin Prime" #31) greatertwinprime "Greater Twin Prime"

#32) isolatedprime "Isolated Prime" #33) lessercousinprime "Lesser Cousin Prime" #34) greatercousinprime "Greater Cousin Prime" #35) lessersexyprime "Lesser Sexy Prime" #36) greatersexyprime "Greater Sexy Prime" #37) eisensteinprime "Eisenstein Prime" #38) gaussianprime "Gaussian Prime" #39) repdigitnum "Rep Digit Number" #40) repunitprime "Rep Unit Prime" #41) woodallnum "Woodall Number"

#42) woodallprime "Woodall Prime" #43) palindromicnum "Palindromic Number" #44) beautifulnum "Beautiful Number" #45) squarenum "Square Number" #46) triangularnum "Triangular Number" #47) oblongnum "Oblong Number" #48) hexagonalnum "Hexagonal Number" #49) tetrahedralnum "Tetrahedral Number" #50) decagonalnum "Decagonal Number" #51) abundantnum "Abundant Number"

#52) aspiringnum "Aspiring Number" #53) sociablenum "Sociable Number" #54) squarefreenum "Square-free Number" #55) luckynum "Lucky Number" #56) luckyprime "Lucky Prime" #57) pentagonalnum "Pentagonal Number" #58) amicablenum "Amicable Number" #59) deficientnum "Deficient Number" #60) happynum "Happy Number" #61) happyprime "Happy Prime" #62) unhappynum "Unhappy Number" #63) unhappyprime "Unhappy Prime" #64) pseudoperfectnum "Pseudo-perfect Number" #65) automorphicnum "Automorphic Number" #66) duffiniannum "Duffinian Number" #67) cuban1prime "Cuban 1 Prime" #68) cuban2prime "Cuban 2 Prime" #69) prothnum "Proth Number" #70) prothprime "Proth Prime" #71) wilsonprime "Wilson Prime"

#72) bellnum "Bell Number" #73) bellprime "Bell Prime" #74) carolnum "Carol Number" #75) carolprime "Carol Prime" #76) cdecagonalnum "Centered Decagonal Number" #77) cdecagonalprime "Centered Decagonal Prime" #78) cheptagonalnum "Centered Heptagonal Number" #79) cheptagonalprime "Centered Heptagonal Prime" #80) csquarenum "Centered Square Number" #81) csquareprime "Centered Square Prime"

#82) ctriangularnum "Centered Triangular Number" #83) ctriangularprime "Centered Triangular Prime" #84) chenprime "Chen Prime" #85) superprime "Super Prime" #86) supersingularprime "Super Singular Prime" #87) cullennum "Cullen Number" #88) cullenprime "Cullen Prime" #89) circularprime "Circular Prime" #90) emirps "Reverse Primes (emirps)" #91) primorialnum "Primorial Number"

#92) primorialprime "Primorial Prime" #93) euclidnum "Euclid Number" #94) euclidprime "Euclid Prime" #95) evenprime "Even Prime" #96) oddprime "Odd Prime" #97) evennum "Even Number" #98) oddnum "Odd Number" #99) fermatnum "Fermat Number" #100) fermatprime "Fermat Prime" #101) genocchiprime "Genochi Prime"

#102) goodprime "Good Prime" #103) kyneanum "Kynea Number" #104) kyneaprime "Kynea Prime" #105) lefttruncatableprime "Left Truncatable Prime" #106) righttruncatableprime "Right Truncatable Prime" #107) twosidedprime "Two Sided Prime" #108) lucasnum "Lucas Number" #109) lucasprime "Lucas Prime" #110) minimalprime "Minimal Prime" #111) padovannum "Padovan Number"

#112) padovanprime "Padovan Prime" #113) partitionnum "Partition Number" #114) partitionprime "Partition Prime" #115) pellnum "Pell Number" #116) pellprime "Pell Prime" #117) perrinnum "Perrin Number" #118) perrinprime "Perrin Prime" #119) pierpontprime "Pierpont Prime" #120) pythagoreanprime "Pythagorean Prime" #121) binaryquadraticprime "Binary Quadratic Prime"

#122) quartanprime "Quartan Prime" #123) residueclass6nplus1prime "Residue Class 6n + 1 Prime" #124) residueclass6nplus5prime "Residue Class 6n + 5 Prime" #125) residueclass8nplus1prime "Residue Class 8n + 1 Prime" #126) residueclass8nplus3prime "Residue Class 8n + 3 Prime" #127) residueclass8nplus5prime "Residue Class 8n + 5 Prime" #128) residueclass8nplus7prime "Residue Class 8n + 7 Prime" #129) residueclass10nplus1prime "Residue Class 10n + 1 Prime" #130) residueclass10nplus3prime "Residue Class 10n + 3 Prime" #131) residueclass10nplus7prime "Residue Class 10n + 7 Prime"

#132) residueclass10nplus9prime "Residue Class 10n + 9 Prime" #133) safeprime "Safe Prime" #134) sophiegermainprime "Sophie Germain Prime" #135) starprime "Star Prime" #136) thabitprime "Thabit Prime" #137) wagstaffformprime "Wagstaff Form of (2p + 1) / 3 Prime" #138) wagstaffvalueprime "Wagstaff Value p Prime"

#139) wieferichbase2prime "Wieferich base 2 prime" #140) wieferichbase3prime "Wieferich base 3 prime" #141) wieferichbase5prime "Wieferich base 5 prime" #142) wieferichbase6prime "Wieferich base 6 prime" #143) wieferichbase7prime "Wieferich base 7 prime" #144) wieferichbase10prime "Wieferich base 10 prime" #145) wieferichbase11prime "Wieferich base 11 prime" #146) wieferichbase12prime "Wieferich base 12 prime" #147) wieferichbase13prime "Wieferich base 13 prime" #148) wieferichbase17prime "Wieferich base 17 prime" #149) wieferichbase19prime "Wieferich base 19 prime"

#150) apocalypticpowernum "Apocalyptic Power Number" #151) cakenum "Cake Number" #152) catalannum "Catalan Number" #153) compositorialnum "Compositorial Number" #154) cubenum "Cube Number" #155) evilnum "Evil Number" #156) factorialnum "Factorial Number" #157) odiousnum "Odious Number" #158) lazycaterernum "Lazy Caterer Number" #159) narcissisticnum "Narcissistic Number" #160) powerof2num "Power of 2 Number" #161) pronicnum "Pronic Number"

> with(inttypes); # Loading the inttypes package (1)

> # Testing Function printtypes > # ======> printtypes(1729); "Composite Number" "3-Almost Prime" "Square-free Number" "Deficient Number" "Unhappy Number" "Proth Number" "Odd Number" "Odious Number" (2) > printtypes(3); "Prime Number" "Mersenne Number" "Mersenne Exponent Prime" "Mersenne Prime" "Fibonacci Number" "Fibonacci Prime" "Permutable Prime" "Lesser Twin Prime" "Lesser Cousin Prime" "Gaussian Prime" "Rep Digit Number" "Palindromic Number" "Beautiful Number" "Triangular Number"

(3) "Square-free Number" "Lucky Number" "Lucky Prime" "Deficient Number" "Unhappy Number" "Unhappy Prime" "Duffinian Number" "Proth Number" "Proth Prime" "Chen Prime" "Super Singular Prime" "Cullen Number" "Cullen Prime" "Circular Prime" "Primorial Prime" "Euclid Number" "Euclid Prime" "Odd Prime" "Odd Number" "Fermat Number" "Fermat Prime" "Left Truncatable Prime" "Right Truncatable Prime" "Two Sided Prime" "Lucas Number" "Lucas Prime" "Minimal Prime" "Padovan Number" "Padovan Prime" "Partition Number" "Partition Prime" "Perrin Number" "Perrin Prime" "Pierpont Prime" "Residue Class 8n C 3 Prime" "Residue Class 10n C 3 Prime" "Sophie Germain Prime" "Super Prime" "Wagstaff Form of (2p C 1) / 3 Prime" "Wagstaff Value p Prime" "Wieferich base 10 prime" "Wieferich base 17 prime"

(3) "Wieferich base 19 prime" "Evil Number" "Narcissistic Number" (3)

> # Testing Maple's ithprime function > # ======> ithprime(25); 97 (4) > ithprime(1); 2 (5) > ithprime(2); 3 (6) > ithprime(3); 5 (7) > ithprime(5); 11 (8) > ithprime(50); 229 (9)

> # Testing function ithcomposite > # ======> ithcomposite(25); 38 (10) > ithcomposite(1); 4 (11) > ithcomposite(2); 6 (12) > ithcomposite(3); 8 (13) > ithcomposite(5); 10 (14) > ithcomposite(50); 70 (15) (3)

> > # Testing function ithprimorial > # ======> ithprimorial(1); 1 (16) > ithprimorial(2); 2 (17) > ithprimorial(3); 6 (18) > ithprimorial(4); 30 (19) > ithprimorial(5); 210 (20) > ithprimorial(6); 2310 (21)

> # Testing Number Theory Types > # ======> # Composite Number - Reference: http://oeis.org/A002808 > # 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88 > for i from 1 to 100 by 1 do > if type(i,compositenum) then printf("%d, ",i); end if; > end do; 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100,

> # Prime: - Reference: http://oeis.org/A000040 > # 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 > for i from 1 to 300 by 1 do > if type(i,prime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, > (3)

>

> > # Semiprime (2-almost prime): - Reference: http://oeis. org/A001358 > # 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187 > for i from 1 to 187 by 1 do > if type(i,semiprime) then printf("%d, ",i); end if; > end do; 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187,

> # 3-almost Prime: - Reference: http://oeis.org/A014612 > # 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244 > for i from 0 to 244 by 1 do > if type(i,almostprime3) then printf("%d, ",i); end if; > end do; 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244,

> # 4-almost Prime: - Reference: http://oeis.org/A014613 > # 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376 > for i from 0 to 376 by 1 do > if type(i,almostprime4) then printf("%d, ",i); end if; > end do; 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376,

> # 5-almost Prime: - Reference: http://oeis.org/A014614 > # 32, 48, 72, 80, 108, 112, 120, 162, 168, 176, 180, 200, 208, 243, 252, 264, 270, 272, 280, 300, 304, 312, 368, 378, 392, 396, 405, 408, 420, 440, 450, 456, 464, 468, 496, 500, 520, 552, 567, 588, 592, 594, 612, 616, 630, 656, 660, 675, 680, 684, 688, 696 > for i from 0 to 696 by 1 do > if type(i,almostprime5) then printf("%d, ",i); end if; (3)

>

>

> end do; 32, 48, 72, 80, 108, 112, 120, 162, 168, 176, 180, 200, 208, 243, 252, 264, 270, 272, 280, 300, 304, 312, 368, 378, 392, 396, 405, 408, 420, 440, 450, 456, 464, 468, 496, 500, 520, 552, 567, 588, 592, 594, 612, 616, 630, 656, 660, 675, 680, 684, 688, 696,

> # 6-almost Prime: - Reference: http://oeis.org/A046306 > # 64, 96, 144, 160, 216, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1320 > for i from 0 to 1320 by 1 do > if type(i,almostprime6) then printf("%d, ",i); end if; > end do; 64, 96, 144, 160, 216, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1320,

> # 7-almost Prime: - Reference: http://oeis.org/A046308 > # 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, 1008, 1056, 1080, 1088, 1120, 1200, 1216, 1248, 1458, 1472, 1512, 1568, 1584, 1620, 1632, 1680, 1760, 1800, 1824, 1856, 1872, 1984, 2000, 2080, 2187, 2208, 2268, 2352, 2368, 2376 > for i from 0 to 2376 by 1 do > if type(i,almostprime7) then printf("%d, ",i); end if; > end do; 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, 1008, 1056, 1080, 1088, 1120, 1200, 1216, 1248, 1458, 1472, 1512, 1568, 1584, 1620, 1632, 1680, 1760, 1800, 1824, 1856, 1872, 1984, 2000, 2080, 2187, 2208, 2268, 2352, 2368, 2376,

> # 8-almost Prime: - Reference: http://oeis.org/A046310 > # 256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4160, 4374, 4416, 4536, 4704, 4736 > for i from 0 to 4736 by 1 do > if type(i,almostprime8) then printf("%d, ",i); end if; > end do; 256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4160, 4374, 4416, 4536, 4704, 4736,

> # 9-almost Prime: - Reference: http://oeis.org/A046312 > # 512, 768, 1152, 1280, 1728, 1792, 1920, 2592, 2688, 2816, 2880, (3)

>

>

>

> 3200, 3328, 3888, 4032, 4224, 4320, 4352, 4480, 4800, 4864, 4992, 5832, 5888, 6048, 6272, 6336, 6480, 6528, 6720, 7040, 7200, 7296, 7424, 7488, 7936, 8000, 8320, 8748, 8832, 9072, 9408 > for i from 0 to 9408 by 1 do > if type(i,almostprime9) then printf("%d, ",i); end if; > end do; 512, 768, 1152, 1280, 1728, 1792, 1920, 2592, 2688, 2816, 2880, 3200, 3328, 3888, 4032, 4224, 4320, 4352, 4480, 4800, 4864, 4992, 5832, 5888, 6048, 6272, 6336, 6480, 6528, 6720, 7040, 7200, 7296, 7424, 7488, 7936, 8000, 8320, 8748, 8832, 9072, 9408,

> # 10-almost Prime: - Reference: http://oeis.org/A046314 > # 1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728, 9984, 11664, 11776, 12096, 12544, 12672, 12960, 13056, 13440, 14080, 14400, 14592, 14848, 14976, 15872, 16000, 16640 > for i from 0 to 9728 by 1 do > if type(i,almostprime10) then printf("%d, ",i); end if; > end do; 1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728,

> # 11-almost Prime: - Reference: http://oeis.org/A069272 > # 2048, 3072, 4608, 5120, 6912, 7168, 7680, 10368, 10752, 11264, 11520, 12800, 13312, 15552, 16128, 16896, 17280, 17408, 17920, 19200, 19456, 19968, 23328, 23552, 24192, 25088, 25344, 25920, 26112, 26880, 28160, 28800, 29184, 29696 > for i from 0 to 7680 by 1 do > if type(i,almostprime11) then printf("%d, ",i); end if; > end do; 2048, 3072, 4608, 5120, 6912, 7168, 7680,

> # 12-almost Prime: - Reference: http://oeis.org/A069273 > # 4096, 6144, 9216, 10240, 13824, 14336, 15360, 20736, 21504, 22528, 23040, 25600, 26624, 31104, 32256, 33792, 34560, 34816, 35840, 38400, 38912, 39936, 46656, 47104, 48384, 50176, 50688, 51840, 52224, 53760, 56320, 57600, 58368, 59392 > for i from 0 to 13824 by 1 do > if type(i,almostprime12) then printf("%d, ",i); end if; > end do; 4096, 6144, 9216, 10240, 13824,

> # 13-almost Prime: - Reference: http://oeis.org/A069274 > # 8192, 12288, 18432, 20480, 27648, 28672, 30720, 41472, 43008, 45056, 46080, 51200, 53248, 62208, 64512, 67584, 69120, 69632, 71680, 76800, 77824, 79872, 93312, 94208, 96768, 100352, 101376, 103680, 104448, 107520, 112640, 115200 > for i from 0 to 27648 by 1 do (3)

>

>

>

>

> if type(i,almostprime13) then printf("%d, ",i); end if; > end do; 8192, 12288, 18432, 20480, 27648,

> # 14-almost Prime: - Reference: http://oeis.org/A069275 > # 16384, 24576, 36864, 40960, 55296, 57344, 61440, 82944, 86016, 90112, 92160, 102400, 106496, 124416, 129024, 135168, 138240, 139264, 143360, 40960, 155648, 159744, 186624, 188416, 193536, 200704, 202752, 207360, 208896, 215040, 225280 > for i from 0 to 55296 by 1 do > if type(i,almostprime14) then printf("%d, ",i); end if; > end do; 16384, 24576, 36864, 40960, 55296,

> # 15-almost Prime: - Reference: http://oeis.org/A069276 > # 32768, 49152, 73728, 81920, 110592, 114688, 122880, 165888, 172032, 180224, 184320, 204800, 212992, 248832, 258048, 270336, 276480, 278528, 286720, 307200, 311296, 319488, 373248, 376832, 387072, 401408, 405504, 414720, 417792, 430080 > for i from 0 to 81920 by 1 do > if type(i,almostprime15) then printf("%d, ",i); end if; > end do; 32768, 49152, 73728, 81920,

> # 16-almost Prime: - Reference: http://oeis.org/A069277 > # 65536, 98304, 147456, 163840, 221184, 229376, 245760, 331776, 344064, 360448, 368640, 409600, 425984, 497664, 516096, 540672, 552960, 557056, 573440, 614400, 622592, 638976, 746496, 753664, 774144, 802816, 811008, 829440, 835584, 860160 > for i from 0 to 163840 by 1 do > if type(i,almostprime16) then printf("%d, ",i); end if; > end do; 65536, 98304, 147456, 163840,

> # 17-almost Prime: - Reference: http://oeis.org/A069278 > # 131072, 196608, 294912, 327680, 442368, 458752, 491520, 663552, 688128, 720896, 737280, 819200, 851968, 995328, 1032192, 1081344, 1105920, 1114112, 1146880, 1228800, 1245184, 1277952, 1492992, 1507328, 1548288, 1605632, 1622016 > if type(131072,almostprime17) then printf("%d, ",i); end if; > if type(196608,almostprime17) then printf("%d, ",i); end if; > if type(294912,almostprime17) then printf("%d, ",i); end if; 163841, 163841, 163841,

> # 18-almost Prime: - Reference: http://oeis.org/A069279 > # 262144, 393216, 589824, 655360, 884736, 917504, 983040, 1327104, 1376256, 1441792, 1474560, 1638400, 1703936, 1990656, 2064384, 2162688, 2211840, 2228224, 2293760, 2457600, 2490368, 2555904, 2985984, 3014656, 3096576 (3)

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> if type(262144,almostprime18) then printf("%d, ",i); end if; > if type(393216,almostprime18) then printf("%d, ",i); end if; > if type(589824,almostprime18) then printf("%d, ",i); end if; 163841, 163841, 163841,

> # 19-almost Prime: - Reference: http://oeis.org/A069280 > # 524288, 786432, 1179648, 1310720, 1769472, 1835008, 1966080, 2654208, 2752512, 2883584, 2949120, 3276800, 3407872, 3981312, 4128768, 4325376, 4423680, 4456448, 4587520, 4915200, 4980736, 5111808, 5971968, 6029312, 6193152 > if type(524288,almostprime19) then printf("%d, ",i); end if; > if type(786432,almostprime19) then printf("%d, ",i); end if; > if type(1179648,almostprime19) then printf("%d, ",i); end if; 163841, 163841, 163841,

> # 20-almost Prime: - Reference: http://oeis.org/A069281 > # 1048576, 1572864, 2359296, 2621440, 3538944, 3670016, 3932160, 5308416, 5505024, 5767168, 5898240, 6553600, 6815744, 7962624, 8257536, 8650752, 8847360, 8912896, 9175040, 9830400, 9961472, 10223616, 11943936, 12058624 > if type(1048576,almostprime20) then printf("%d, ",i); end if; > if type(1572864,almostprime20) then printf("%d, ",i); end if; > if type(2359296,almostprime20) then printf("%d, ",i); end if; 163841, 163841, 163841,

> # Perfect Number: - Reference: http://oeis.org/A000396 > # 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216 > for i from 1 to 8128 by 1 do > if type(i,perfectnum) then printf("%d, ",i); end if; > end do; 6, 28, 496, 8128,

> # Mersenne Number: - Reference: http://oeis.org/A000225 > # 0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295 > for i from 0 to 16383 by 1 do > if type(i,mersennenum) then printf("%d, ",i); end if; > end do; 0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383,

> # Mersenne Prime: - Reference: http://oeis.org/A000668 > # 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, (3)

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170141183460469231731687303715884105727 > for i from 0 to 10000 by 1 do > if type(i,mersenneprime) then printf("%d, ",i); end if; > end do; 3, 7, 31, 127, 8191,

> # Mersenne Exponent Prime: - Reference: http://oeis.org/A000043 > # 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011 > for i from 1 to 100000 by 1 do > if type(i,mersenneexpprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243,

> # Fibonacci Number: - Reference: http://oeis.org/A000045 > # 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169 > for i from 0 to 10000 by 1 do > if type(i,fibonaccinum) then printf("%d, ",i); end if; > end do; 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765,

> # Fibonacci Prime: - Reference: http://oeis.org/A005478 > # 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376 935476241 > for i from 0 to 10000 by 1 do > if type(i,fibonacciprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 13, 89, 233, 1597,

> # Permutable Prime: - Reference: http://oeis.org/A003459 > # 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, 1111111111111111111, 11111111111111111111111 > for i from 9 to 100 by 1 do > if type(i,permutableprime) then printf("%d, ",i); end if; > end do; 11, 13, 17, 31, 37, 71, 73, 79, 97,

> # Lesser Twin Prime: - Reference: http://oeis.org/A001359 (3)

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> # 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607 > for i from 0 to 2000 by 1 do > if type(i,lessertwinprime) then printf("%d, ",i); end if; > end do; 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607, 1619, 1667, 1697, 1721, 1787, 1871, 1877, 1931, 1949, 1997,

> # Greater Twin Prime: - Reference: http://oeis.org/A006512 > # 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609 > for i from 0 to 2000 by 1 do > if type(i,greatertwinprime) then printf("%d, ",i); end if; > end do; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609, 1621, 1669, 1699, 1723, 1789, 1873, 1879, 1933, 1951, 1999,

> # Lesser Cousin Prime: - Reference: http://oeis.org/A023200 > # 3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483 > for i from 0 to 1483 by 1 do > if type(i,lessercousinprime) then printf("%d, ",i); end if; > end do; 3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483,

> # Greater Cousin Prime: - Reference: http://oeis.org/A046132 > # 7, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433 > for i from 0 to 1433 by 1 do > if type(i,greatercousinprime) then printf("%d, ",i); end if; (3)

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> end do; 7, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433,

> # Lesser Sexy Prime: - Reference: http://oeis.org/A023201 > # 5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571, 587, 593, 601, 607, 613, 641, 647 > for i from 0 to 647 by 1 do > if type(i,lessersexyprime) then printf("%d, ",i); end if; > end do; 5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571, 587, 593, 601, 607, 613, 641, 647,

> # Greater Sexy Prime: - Reference: http://oeis.org/A046117 > # 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137, 157, 163, 173, 179, 197, 199, 229, 233, 239, 257, 263, 269, 277, 283, 313, 317, 337, 353, 359, 373, 379, 389, 439, 449, 463, 467, 509, 547, 563, 569, 577, 593, 599, 607, 613 > for i from 0 to 613 by 1 do > if type(i,greatersexyprime) then printf("%d, ",i); end if; > end do; 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137, 157, 163, 173, 179, 197, 199, 229, 233, 239, 257, 263, 269, 277, 283, 313, 317, 337, 353, 359, 373, 379, 389, 439, 449, 463, 467, 509, 547, 563, 569, 577, 593, 599, 607, 613,

> # Eisenstein Prime: - Reference: http://oeis.org/A003627 > # 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569, 587 > for i from 0 to 587 by 1 do > if type(i,eisensteinprime) then printf("%d, ",i); end if; > end do; 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569, 587, (3)

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> # Gaussian Prime: - Reference: http://oeis.org/A002145 > # 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 571 > for i from 0 to 571 by 1 do > if type(i,gaussianprime) then printf("%d, ",i); end if; > end do; 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 571,

> # Rep Digit Number: - Reference: http://oeis.org/A010785 > # 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222 > for i from 0 to 3333 by 1 do > if type(i,repdigitnum) then printf("%d, ",i); end if; > end do; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333,

> # Rep Unit Prime: - Reference: http://oeis.org/A004022 > # 11, 1111111111111111111, 11111111111111111111111 > type(11,repunitprime); > type(1111111111111111111,repunitprime); > type(11111111111111111111111,repunitprime); true true true (22)

> # Woodall Number: - Reference: http://oeis.org/A003261 > # 1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519, 44040191, 92274687, 192937983, 402653183, 838860799, 1744830463, 3623878655, 7516192767 > for i from 0 to 22527 by 1 do > if type(i,woodallnum) then printf("%d, ",i); end if; > end do; 1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527,

> # Woodall Prime: - Reference: http://oeis.org/A050918 > # 7, 23, 383, 32212254719, 2833419889721787128217599, 195845982777569926302400511, (3)

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> 4776913109852041418248056622882488319, 1307960347852357218937346147315859062783, 225251798594466661409915431774713195745814267044878909733007331390 393510002687 > for i from 0 to 500 by 1 do > if type(i,woodallprime) then printf("%d, ",i); end if; > end do; 7, 23, 383, > type (22525179859446666140991543177471319574581426704487890973300733139 0393510002687, woodallprime); true (23)

> # Palindromic Number: - Reference: http://oeis.org/A002113 > # 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515 > for i from 0 to 515 by 1 do > if type(i,palindromicnum) then printf("%d, ",i); end if; > end do; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515,

> > # Beautiful Number: - Reference: http://oeis.org/A032799 > # 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427, 2646798, 12157692622039623539 > for i from 0 to 2427 by 1 do > if type(i,beautifulnum) then printf("%d, ",i); end if; > end do; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427,

> # Square Number: - Reference: http://oeis.org/A000290 > # 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849 > for i from 0 to 1849 by 1 do > if type(i,squarenum) then printf("%d, ",i); end if; > end do; 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, (3)

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> # Triangular Number: - Reference: http://oeis.org/A000217 > # 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431 > for i from 0 to 1431 by 1 do > if type(i,triangularnum) then printf("%d, ",i); end if; > end do; 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431,

> # Oblong Number: - Reference: http://oeis.org/A002378 > # 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550 > for i from 0 to 2550 by 1 do > if type(i,oblongnum) then printf("%d, ",i); end if; > end do; 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550,

> # Hexagonal Number: - Reference: http://oeis.org/A000384 > # 0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560 > for i from 0 to 4560 by 1 do > if type(i,hexagonalnum) then printf("%d, ",i); end if; > end do; 0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560,

> # Tetrahedral Number: - Reference: http://oeis.org/A000292 > # 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180 > for i from 0 to 15180 by 1 do > if type(i,tetrahedralnum) then printf("%d, ",i); end if; > end do; (3)

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0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180,

> # Decagonal Number: - Reference: http://oeis.org/A001107 > # 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326 > for i from 0 to 8326 by 1 do > if type(i,decagonalnum) then printf("%d, ",i); end if; > end do; 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326,

> # Abundant Number: - Reference: http://oeis.org/A005101 > # 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270 > for i from 0 to 270 by 1 do > if type(i,abundantnum) then printf("%d, ",i); end if; > end do; 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270,

> # Aspiring Number: - Reference: http://oeis.org/A063769 > # 25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685 > for i from 0 to 685 by 1 do > if type(i,aspiringnum) then printf("%d, ",i); end if; > end do; 25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685,

> # Sociable Number: - Reference: http://oeis.org/A122726 > # 12496, 14264, 14288, 14316, 14536, 15472, 17716, 19116, 19916, 22744, 22976, 31704, 45946, 47616, 48976, 83328, 97946, 122410, 152990, 177792, 243760, 274924, 275444, 285778, 294896, 295488, 358336, 366556, 376736, 381028, 418904, 589786 > for i from 1 to 31704 by 1 do > if type(i, sociablenum) then printf("%d, ",i); end if; > end do; 12496, 14264, 14288, 14316, 14536, 15472, 17716, 19116, 19916, (3)

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22744, 22976, 31704,

> # Apocalyptic Power Number: - Reference: http://oeis.org/A007356 > # 157, 192, 218, 220, 222, 224, 226, 243, 245, 247, 251, 278, 285, 286, 287, 312, 355, 361, 366, 382, 384, 390, 394, 411, 434, 443, 478, 497, 499, 506, 508, 528, 529, 539, 540, 541, 564, 578, 580, 582, 583, 610 > for i from 1 to 610 by 1 do > if type(i, apocalypticpowernum) then printf("%d, ",i); end if; > end do; 157, 192, 218, 220, 222, 224, 226, 243, 245, 247, 251, 278, 285, 286, 287, 312, 355, 361, 366, 382, 384, 390, 394, 411, 434, 443, 478, 497, 499, 506, 508, 528, 529, 539, 540, 541, 564, 578, 580, 582, 583, 610,

> # Cake Number: - Reference: http://oeis.org/A000125 > # 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, 9178, 9920, 10701, 11522, 12384, 13288, 14235, 15226 > for i from 0 to 15300 by 1 do > if type(i, cakenum) then printf("%d, ",i); end if; > end do; 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, 9178, 9920, 10701, 11522, 12384, 13288, 14235, 15226,

> # Catalan Number: - Reference: http://oeis.org/A000108 > # 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304 > for i from 0 to 58786 by 1 do > if type(i, catalannum) then printf("%d, ",i); end if; > end do; 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786,

> # Compositorial Number: - Reference: http://oeis.org/A036691 > # 1, 4, 24, 192, 1728, 17280, 207360, 2903040, 43545600, 696729600, 12541132800, 250822656000, 5267275776000, 115880067072000, 2781121609728000, 69528040243200000, 1807729046323200000, 48808684250726400000, 1366643159020339200000 > for i from 1 to 207360 by 1 do > if type(i, compositorialnum) then printf("%d, ",i); end if; > end do; 1, 4, 24, 192, 1728, 17280, 207360, (3)

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> # Cube Number: - Reference: http://oeis.org/A000578 > # 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000 > for i from 0 to 64000 by 1 do > if type(i, cubenum) then printf("%d, ",i); end if; > end do; 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000,

> # Automorphicnum Number (Curious Number): - Reference: http://oeis.org/A003226 > # 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 8212890625, 18212890625, 81787109376, 918212890625, 9918212890625, 40081787109376, 59918212890625 > for i from 0 to 90625 by 1 do > if type(i, automorphicnum) then printf("%d, ",i); end if; > end do; 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625,

> # Evil Number: - Reference: http://oeis.org/A001969 > # 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 63, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 95, 96, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 129 > for i from 0 to 129 by 1 do > if type(i, evilnum) then printf("%d, ",i); end if; > end do; 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 63, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 95, 96, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 129,

> # Odious Number: - Reference: http://oeis.org/A000069 > # 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 64, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 97, 98, 100, 103, 104, 107, 109, 110, 112, 115, 117, 118, 121, 122, 124, 127, 128 > for i from 0 to 129 by 1 do > if type(i, odiousnum) then printf("%d, ",i); end if; > end do; 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 64, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 97, (3)

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98, 100, 103, 104, 107, 109, 110, 112, 115, 117, 118, 121, 122, 124, 127, 128,

> # Factorial Number: - Reference: http://oeis.org/A000142 > # 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000 > for i from 0 to 40320 by 1 do > if type(i, factorialnum) then printf("%d, ",i); end if; > end do; 1, 2, 6, 24, 120, 720, 5040, 40320,

> # Lazy Caterer Number: - Reference: http://oeis.org/A000124 > # 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379 > for i from 0 to 1379 by 1 do > if type(i, lazycaterernum) then printf("%d, ",i); end if; > end do; 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379,

> # Narcissistic Number (Plus Perfect Number): - Reference: http://oeis.org/A005188 > # 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315, 24678050, 24678051, 88593477, 146511208, 472335975, 534494836, 912985153, 4679307774, 32164049650, 32164049651 > for i from 0 to 93084 by 1 do > if type(i, narcissisticnum) then printf("%d, ",i); end if; > end do; 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084,

> # Power of 2 Number: - Reference: http://oeis.org/A000079 > # 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592 > for i from 0 to 32768 by 1 do > if type(i, powerof2num) then printf("%d, ",i); end if; > end do; 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, (3)

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> > # Pronic Number (Heteromecic Number): - Reference: http://oeis. org/A002378 > # 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550 > for i from 0 to 2550 by 1 do > if type(i, pronicnum) then printf("%d, ",i); end if; > end do; 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550,

> # Square-free Number: - Reference: http://oeis.org/A005117 > # 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113 > for i from 0 to 113 by 1 do > if type(i, squarefreenum) then printf("%d, ",i); end if; > end do; 0, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113,

> # Lucky Number: - Reference: http://oeis.org/A000959 > # 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303 > for i from 0 to 303 by 1 do > if type(i, luckynum) then printf("%d, ",i); end if; > end do; 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303,

> # Lucky Prime: - Reference: http://oeis.org/A031157 > # 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123 > for i from 0 to 1123 by 1 do > if type(i, luckyprime) then printf("%d, ",i); end if; (3)

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> end do; 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123,

> # Pentagonal Number: - Reference: http://oeis.org/A000326 > # 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151 > for i from 0 to 3151 by 1 do > if type(i, pentagonalnum) then printf("%d, ",i); end if; > end do; 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151,

> # Amicable Number: - Reference: http://oeis.org/A063990 > # 220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 67095, 69615, 71145, 76084, 79750, 87633, 88730, 100485, 122265, 122368, 123152, 124155, 139815, 141664, 142310 > for i from 0 to 67095 by 1 do > if type(i, amicablenum) then printf("%d, ",i); end if; > end do; 220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 67095,

> # Deficient Number: - Reference: http://oeis.org/A005100 > # 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86 > for i from 0 to 86 by 1 do > if type(i, deficientnum) then printf("%d, ",i); end if; > end do; 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86,

> # Happy Number: - Reference: http://oeis.org/A007770 > # 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338 > for i from 0 to 338 by 1 do > if type(i, happynum) then printf("%d, ",i); end if; (3)

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> end do; 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338,

> > # Happy Prime: - Reference: http://oeis.org/A035497 > # 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093, 1151, 1277, 1303, 1373, 1427, 1447, 1481, 1487, 1511, 1607, 1663 > for i from 0 to 1663 by 1 do > if type(i, happyprime) then printf("%d, ",i); end if; > end do; 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093, 1151, 1277, 1303, 1373, 1427, 1447, 1481, 1487, 1511, 1607, 1663,

> # Unhappy Number: - Reference: http://oeis.org/A031177 > # 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81 > for i from 0 to 81 by 1 do > if type(i, unhappynum) then printf("%d, ",i); end if; > end do; 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81,

> # Unhappy Prime: - Reference: http://oeis.org/A094480 > # 2, 3, 5, 11, 17, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 101, 107, 113, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 269, 271, 277, 281, 283, 307, 311, 317, 337, 347, 349, 353, 359, 373 > for i from 0 to 373 by 1 do > if type(i, unhappyprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 11, 17, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 101, 107, 113, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 269, 271, 277, 281, 283, 307, 311, 317, 337, 347, 349, 353, 359, 373, (3)

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> > # Pseudo-perfect Number: - Reference: http://oeis.org/A005835 > # 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264 > for i from 0 to 234 by 1 do > if type(i, pseudoperfectnum) then printf("%d, ",i); end if; > end do; 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234,

> # Duffinian Number: - Reference: http://oeis.org/A014567 > # 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 47, 49, 50, 53, 55, 57, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 89, 93, 97, 98, 100, 101, 103, 107, 109, 111, 113, 115, 119, 121, 125, 127, 128, 129, 131, 133 > for i from 0 to 133 by 1 do > if type(i, duffiniannum) then printf("%d, ",i); end if; > end do; 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 47, 49, 50, 53, 55, 57, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 89, 93, 97, 98, 100, 101, 103, 107, 109, 111, 113, 115, 119, 121, 125, 127, 128, 129, 131, 133,

> # Cuban 1 Prime: - Reference: http://oeis.org/A002407 > # 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227 > for i from 0 to 6211 by 1 do > if type(i, cuban1prime) then printf("%d, ",i); end if; > end do; 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211,

> # Cuban 2 Prime: - Reference: http://oeis.org/A002648 > # 13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313, 73009, 76801, 84673, 106033, 108301, 112909, 115249, 129793, 139969 > for i from 0 to 43201 by 1 do > if type(i, cuban2prime) then printf("%d, ",i); end if; > end do; 13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, (3)

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> # Proth Number: - Reference: http://oeis.org/A080075 > # 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1025, 1089, 1153, 1217, 1281, 1345, 1409 > for i from 0 to 1409 by 1 do > if type(i, prothnum) then printf("%d, ",i); end if; > end do; 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1025, 1089, 1153, 1217, 1281, 1345, 1409,

> # Proth Prime: - Reference: http://oeis.org/A080076 > # 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857, 10369, 10753, 11393, 11777, 12161, 12289, 13313 > for i from 0 to 13313 by 1 do > if type(i, prothprime) then printf("%d, ",i); end if; > end do; 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857, 10369, 10753, 11393, 11777, 12161, 12289, 13313,

> # Wilson Prime: - Reference: http://oeis.org/A007540 > # 5, 13, 563 > for i from 0 to 1000 by 1 do > if type(i, wilsonprime) then printf("%d, ",i); end if; > end do; 5, 13, 563,

> # Bell Number: - Reference: http://oeis.org/A000110 > # 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346 > for i from 0 to 21147 by 1 do > if type(i, bellnum) then printf("%d, ",i); end if; > end do; 1, 2, 5, 15, 52, 203, 877, 4140, 21147,

> # Bell Prime: - Reference: http://oeis.org/A051131 > # 2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837 > for i from 0 to 877 by 1 do (3)

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> # Carol Number: - Reference: http://oeis.org/A093112 > # -1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, 4190207, 16769023, 67092479, 268402687, 1073676287, 4294836223, 17179607039, 68718952447, 274876858367, 1099509530623, 4398042316799, 17592177655807 > for i from -50 to 16127 by 1 do > if type(i, carolnum) then printf("%d, ",i); end if; > end do; -1, 7, 47, 223, 959, 3967, 16127,

> # Carol Prime: - Reference: http://oeis.org/A091516 > # 7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087 > for i from -50 to 261119 by 1 do > if type(i,carolprime) then printf("%d, ",i); end if; > end do; 7, 47, 223, 3967, 16127,

> # Centered Decagonal Number: - Reference: http://oeis.org/A062786 > # 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901 > for i from 0 to 9901 by 1 do > if type(i,cdecagonalnum) then printf("%d, ",i); end if; > end do; 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901,

> # Centered Decagonal Prime: - Reference: http://oeis.org/A090562 > # 11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281, 6301, 6661, 7411, 9461, 9901, 12251, 13781, 14851, 15401, 18301, 18911, 19531, 20161, 22111, 24151, 24851, 25561, 27011, 27751 > for i from 0 to 27751 by 1 do > if type(i,cdecagonalprime) then printf("%d, ",i); end if; > end do; 11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281, 6301, 6661, 7411, 9461, 9901, 12251, 13781, 14851, 15401, 18301, 18911, 19531, 20161, 22111, 24151, 24851, 25561, 27011, 27751, (3)

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> > # Centered Heptagonal Number: - Reference: http://oeis. org/A069099 > # 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246 > for i from 0 to 7246 by 1 do > if type(i,cheptagonalnum) then printf("%d, ",i); end if; > end do; 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246,

> # Centered Heptagonal Prime: - Reference: http://oeis.org/A144974 > # 43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 9283, 10781, 11173, 12391, 14561, 18397, 20483, 29303, 29947, 34651, 37493, 41203, 46691, 50821, 54251, 56897, 57793, 65213, 68111, 72073, 76147, 84631, 89041 > for i from 0 to 89041 by 1 do > if type(i,cheptagonalprime) then printf("%d, ",i); end if; > end do; 43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 9283, 10781, 11173, 12391, 14561, 18397, 20483, 29303, 29947, 34651, 37493, 41203, 46691, 50821, 54251, 56897, 57793, 65213, 68111, 72073, 76147, 84631, 89041,

> # Centered Square Number: - Reference: http://oeis.org/A001844 > # 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325 > for i from 0 to 4325 by 1 do > if type(i,csquarenum) then printf("%d, ",i); end if; > end do; 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325,

> # Centered Square Prime: - Reference: http://oeis.org/A027862 > # 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, 4513, 5101, 7321, 8581, 9661, 9941, 10513, 12641, 13613, 14281, 14621, 15313, 16381, 19013, 19801, 20201, 21013, 21841, 23981, 24421, 26681 > for i from 0 to 26681 by 1 do > if type(i,csquareprime) then printf("%d, ",i); end if; > end do; 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, 4513, 5101, 7321, (3)

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8581, 9661, 9941, 10513, 12641, 13613, 14281, 14621, 15313, 16381, 19013, 19801, 20201, 21013, 21841, 23981, 24421, 26681,

> # Centered Triangular Number: - Reference: http://oeis. org/A144974 > # 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, 3106, 3244, 3385, 3529 > for i from 0 to 3529 by 1 do > if type(i,ctriangularnum) then printf("%d, ",i); end if; > end do; 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, 3106, 3244, 3385, 3529,

> # Centered Triangular Prime: - Reference: http://oeis.org/A125602 > # 19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459, 10711, 13681, 14851, 16069, 16381, 17659, 20011, 20359, 23251, 25939, 27541, 29191, 29611, 31321, 34429, 36739, 40099, 40591, 42589 > for i from 0 to 42589 by 1 do > if type(i,ctriangularprime) then printf("%d, ",i); end if; > end do; 19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459, 10711, 13681, 14851, 16069, 16381, 17659, 20011, 20359, 23251, 25939, 27541, 29191, 29611, 31321, 34429, 36739, 40099, 40591, 42589,

> # Chen Prime: - Reference: http://oeis.org/A109611 > # 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409 > for i from 0 to 409 by 1 do > if type(i,chenprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409,

> # Super Prime: - Reference: http://oeis.org/A006450 > # 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, (3)

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> 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1433, 1447, 1471 > for i from 0 to 1471 by 1 do > if type(i,superprime) then printf("%d, ",i); end if; > end do; 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1433, 1447, 1471,

> # Super Singular Prime: - Reference: http://oeis.org/A002267 > # 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 > for i from 0 to 100 by 1 do > if type(i,supersingularprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71,

> > # Cullen Number: - Reference: http://oeis.org/A002064 > # 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521, 44040193, 92274689, 192937985, 402653185, 838860801, 1744830465, 3623878657, 7516192769, 15569256449, 32212254721 > for i from 0 to 49153 by 1 do > if type(i,cullennum) then printf("%d, ",i); end if; > end do; 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153,

> # Cullen Prime: - Reference: http://oeis.org/A050920 > # 3, 393050634124102232869567034555427371542904833 > for i from 0 to 1000 by 1 do > if type(i,cullenprime) then printf("%d, ",i); end if; > end do; 3, > type(393050634124102232869567034555427371542904833, cullenprime); true (24)

> # Circular Prime: - Reference: http://oeis.org/A068652 > # 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993 > for i from 0 to 3119 by 1 do > if type(i,circularprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, (3)

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> # Reverse Primes (emirps): - Reference: http://oeis.org/A006567 > # 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193 > for i from 0 to 1193 by 1 do > if type(i,emirps) then printf("%d, ",i); end if; > end do; 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193,

> # Primorial Number: - Reference: http://oeis.org/A002064 > # 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070 > for i from 0 to 30030 by 1 do > if type(i,primorialnum) then printf("%d, ",i); end if; > end do; 1, 2, 6, 30, 210, 2310, 30030,

> # Primorial Prime: - Reference: http://oeis.org/A057705 union http://oeis.org/A018239 > # 3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309 > for i from 0 to 30029 by 1 do > if type(i,primorialprime) then printf("%d, ",i); end if; > end do; 3, 5, 7, 29, 31, 211, 2309, 2311, 30029,

> # Euclid Number: - Reference: http://oeis.org/A006862 minus {2} > # 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, 6469693231, 200560490131, 7420738134811, 304250263527211, 13082761331670031, 614889782588491411, 32589158477190044731, 1922760350154212639071 > for i from 0 to 30031 by 1 do > if type(i,euclidnum) then printf("%d, ",i); end if; > end do; 3, 7, 31, 211, 2311, 30031,

> # Euclid Prime: - Reference: http://oeis.org/A018239 minus {2} > # 3, 7, 31, 211, 2311, 200560490131, > for i from 0 to 2311 by 1 do > if type(i,euclidprime) then printf("%d, ",i); end if; (3)

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> # Even Number: - Reference:http://oeis.org/A005843 > # 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120 > for i from 0 to 120 by 1 do > if type(i,evennum) then printf("%d, ",i); end if; > end do; 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120,

> # Odd Number: - Reference: http://oeis.org/A005408 > # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131 > for i from 0 to 131 by 1 do > if type(i,oddnum) then printf("%d, ",i); end if; > end do; 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131,

> # Even Prime: - Reference: (The only even prime is 2) > # 2 > for i from 0 to 300 by 1 do > if type(i,evenprime) then printf("%d, ",i); end if; > end do; 2,

> # Odd Prime: - Reference: http://oeis.org/A065091 > # 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 > for i from 0 to 271 by 1 do > if type(i,oddprime) then printf("%d, ",i); end if; > end do; 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, (3)

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> # Fermat Number: - Reference: http://oeis.org/A000215 > # 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457 > for i from 0 to 65537 by 1 do > if type(i,fermatnum) then printf("%d, ",i); end if; > end do; 3, 5, 17, 257, 65537,

> # Fermat Prime: - Reference: http://oeis.org/A019434 > # 3, 5, 17, 257, 65537 > for i from 0 to 65537 by 1 do > if type(i,fermatprime) then printf("%d, ",i); end if; > end do; 3, 5, 17, 257, 65537,

> # Genochi Prime: - Reference: (The only positive prime Genocchi number is 17) > # 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 > for i from 0 to 271 by 1 do > if type(i,genocchiprime) then printf("%d, ",i); end if; > end do; 17,

> # Good Prime: - Reference: http://oeis.org/A028388 > # 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541, 557, 563, 569, 587, 593, 599, 641, 727, 733, 739, 809, 821, 853, 929, 937, 967, 1009, 1031, 1087, 1151, 1213, 1277 > for i from 1 to 541 by 1 do > if type(i,goodprime) then printf("%d, ",i); end if; > end do; 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541,

> # Kynea Number: - Reference: http://oeis.org/A093069 > # 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023 > for i from 0 to 66047 by 1 do > if type(i,kyneanum) then printf("%d, ",i); end if; > end do; 7, 23, 79, 287, 1087, 4223, 16639, 66047, (3)

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> # Kynea Prime: - Reference: http://oeis.org/A091514 > # 7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359, 17180131327, 68720001023, 4398050705407, 70368760954879, 18014398777917439, 18446744082299486207, 5070602400912922109586440191999 > for i from 0 to 66047 by 1 do > if type(i,kyneaprime) then printf("%d, ",i); end if; > end do; 7, 23, 79, 1087, 66047,

> # Left Truncatable Prime: - Reference: http://oeis.org/A028388 > # 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 937, 947, 953, 967, 983, 997, 1223 > for i from 0 to 1223 by 1 do > if type(i,lefttruncatableprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 937, 947, 953, 967, 983, 997, 1223,

> # Right Truncatable Prime: - Reference: http://oeis.org/A024770 > # 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193 > for i from 0 to 31193 by 1 do > if type(i,righttruncatableprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193,

> # Two Sided Prime: - Reference: http://oeis.org/A020994 > # 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397 > for i from 0 to 3797 by 1 do > if type(i,twosidedprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797,

> # Lucas Number: - Reference: http://oeis.org/A000032 (3)

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> # 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282 > for i from 3 to 9349 by 1 do > if type(i,lucasnum) then printf("%d, ",i); end if; > end do; 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, > type(0,lucasnum); # 2 if i = 0 true (25)

> type(1,lucasnum); # 1 if i = 1 true (26)

> # L[i-1] + L[i-2] if i > 1

> # Lucas Prime: - Reference: http://oeis.org/A005479 > # 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771 > for i from 0 to 9349 by 1 do > if type(i,lucasprime) then printf("%d, ",i); end if; > end do; 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349,

> # Minimal Prime: - Reference: http://oeis.org/A071062 > # 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 > for i from 0 to 9949 by 1 do > if type(i,minimalprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949,

> # Padovan Number: - Reference: http://oeis.org/A000931 > # 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625 > for i from 0 to 1432 by 1 do > if type(i,padovannum) then printf("%d, ",i); end if; > end do; 1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432,

> # Padovan Prime: - Reference: http://oeis.org/A100891 > # 2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, (3)

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> 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 155887769514160850775109894189926597511540361862181195186859880916 4180630185566719 > for i from 0 to 3329 by 1 do > if type(i,padovanprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 37, 151, 3329,

> # Partition Number: - Reference: http://oeis.org/A000041 > # 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134 > for i from 0 to 89134 by 1 do > if type(i,partitionnum) then printf("%d, ",i); end if; > end do; 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134,

> # Partition Prime: - Reference: http://oeis.org/A049575 > # 2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557 > for i from 0 to 17977 by 1 do > if type(i,partitionprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 11, 101, 17977,

> # Pell Number: - Reference: http://oeis.org/A000129 > # 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, 18457556052, 44560482149 > for i from 0 to 5741 by 1 do > if type(i,pellnum) then printf("%d, ",i); end if; > end do; 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741,

> # Pell Prime: - Reference: http://oeis.org/A086383 > # 2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281 > for i from 0 to 33461 by 1 do > if type(i,pellprime) then printf("%d, ",i); end if; (3)

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> end do; 2, 5, 29, 5741, 33461,

> # Perrin Number: - Reference: http://oeis.org/A001608 > # 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486, 644, 853, 1130, 1497, 1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 43721, 57918, 76725, 101639, 134643, 178364, 236282, 313007 > for i from 0 to 3480 by 1 do > if type(i,perrinnum) then printf("%d, ",i); end if; > end do; 0, 2, 3, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486, 644, 853, 1130, 1497, 1983, 2627, 3480,

> # Perrin Prime: - Reference: http://oeis.org/A074788 > # 2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797, > for i from 0 to 14197 by 1 do > if type(i,perrinprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 17, 29, 277, 367, 853, 14197,

> # Pierpont Prime: - Reference: http://oeis.org/A005109 > # 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 10369, 12289, 17497, 18433, 39367, 52489, 65537, 139969, 147457, 209953, 331777, 472393, 629857, 746497, 786433, 839809, 995329 > for i from 0 to 433 by 1 do > if type(i,pierpontprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433,

> # Pythagorean Prime: - Reference: http://oeis.org/A002144 > # 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 601, 613, 617 > for i from 0 to 281 by 1 do > if type(i,pythagoreanprime) then printf("%d, ",i); end if; > end do; 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281,

> # Binary Quadratic Prime: - Reference: http://oeis.org/A106856 > # 2, 11, 23, 37, 43, 53, 71, 79, 107, 109, 127, 137, 149, 151, 163, 193, 197, 211, 233, 239, 263, 281, 317, 331, 337, 373, 389, (3)

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> 401, 421, 431, 443, 463, 487, 491, 499, 541, 547, 557, 569, 599, 613, 617, 641, 653, 659, 673, 683, 739, 743, 751, 757, 809, 821 > for i from 0 to 401 by 1 do > if type(i,binaryquadraticprime) then printf("%d, ",i); end if; > end do; 2, 11, 23, 37, 43, 53, 71, 79, 107, 109, 127, 137, 149, 151, 163, 193, 197, 211, 233, 239, 263, 281, 317, 331, 337, 373, 389, 401,

> # Quartan Prime: - Reference: http://oeis.org/A002645 > # 2, 17, 97, 257, 337, 641, 881, 1297, 2417, 2657, 3697, 4177, 4721, 6577, 10657, 12401, 14657, 14897, 15937, 16561, 28817, 38561, 39041, 49297, 54721, 65537, 65617, 66161, 66977, 80177, 83537, 83777, 89041, 105601, 107377, 119617, 121937 > for i from 0 to 1297 by 1 do > if type(i,quartanprime) then printf("%d, ",i); end if; > end do; 2, 17, 97, 257, 337, 641, 881, 1297,

> # Residue Class 6n + 1 Prime: - Reference: http://oeis. org/A0024768 > # 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619 > for i from 0 to 619 by 1 do > if type(i,residueclass6nplus1prime) then printf("%d, ",i); end if; > end do; 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619,

> # Residue Class 6n + 5 Prime: - Reference: http://oeis. org/A007528 > # 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569 > for i from 0 to 569 by 1 do > if type(i,residueclass6nplus5prime) then printf("%d, ",i); end if; > end do; 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569, (3)

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> > # Residue Class 8n + 1 Prime: - Reference: http://oeis. org/A007519 > # 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641, 673, 761, 769, 809, 857, 881, 929, 937, 953, 977, 1009, 1033, 1049, 1097, 1129, 1153, 1193, 1201, 1217, 1249, 1289, 1297, 1321, 1361 > for i from 0 to 641 by 1 do > if type(i,residueclass8nplus1prime) then printf("%d, ",i); end if; > end do; 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641,

> # Residue Class 8n + 3 Prime: - Reference: http://oeis. org/A007520 > # 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 587, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 883, 907, 947, 971, 1019, 1051, 1091, 1123, 1163, 1171, 1187 > for i from 0 to 547 by 1 do > if type(i,residueclass8nplus3prime) then printf("%d, ",i); end if; > end do; 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547,

> # Residue Class 8n + 5 Prime: - Reference: http://oeis. org/A007521 > # 5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269, 277, 293, 317, 349, 373, 389, 397, 421, 461, 509, 541, 557, 613, 653, 661, 677, 701, 709, 733, 757, 773, 797, 821, 829, 853, 877, 941, 997, 1013, 1021, 1061, 1069, 1093, 1109 > for i from 0 to 557 by 1 do > if type(i,residueclass8nplus5prime) then printf("%d, ",i); end if; > end do; 5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269, 277, 293, 317, 349, 373, 389, 397, 421, 461, 509, 541, 557,

> # Residue Class 8n + 7 Prime: - Reference: http://oeis. org/A007522 > # 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991, 1031, 1039, 1063, 1087, 1103, 1151 > for i from 0 to 599 by 1 do > if type(i,residueclass8nplus7prime) then printf("%d, ",i); end if; (3)

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> end do; 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599,

> # Residue Class 10n + 1 Prime: - http://oeis.org/A030430 > # 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631, 641, 661, 691, 701, 751, 761, 811, 821, 881, 911, 941, 971, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231, 1291 > for i from 0 to 631 by 1 do > if type(i,residueclass10nplus1prime) then printf("%d, ",i); end if; > end do; 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631,

> # Residue Class 10n + 3 Prime: - Reference: http://oeis. org/A030431 > # 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593, 613, 643, 653, 673, 683, 733, 743, 773, 823, 853, 863, 883, 953, 983, 1013, 1033, 1063, 1093, 1103, 1123, 1153, 1163, 1193 > for i from 0 to 593 by 1 do > if type(i,residueclass10nplus3prime) then printf("%d, ",i); end if; > end do; 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593,

> # Residue Class 10n + 7 Prime: - Reference: http://oeis. org/A030432 > # 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217, 1237 > for i from 0 to 577 by 1 do > if type(i,residueclass10nplus7prime) then printf("%d, ",i); end if; > end do; 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577,

> # Residue Class 10n + 9 Prime: - Reference: http://oeis. org/A030433 > # 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, (3)

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> 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619, 659, 709, 719, 739, 769, 809, 829, 839, 859, 919, 929, 1009, 1019, 1039, 1049, 1069, 1109, 1129, 1229, 1249, 1259, 1279, 1289 > for i from 0 to 619 by 1 do > if type(i,residueclass10nplus9prime) then printf("%d, ",i); end if; > end do; 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619,

> # Safe Prime: - Reference: http://oeis.org/A005385 > # 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903 > for i from 0 to 479 by 1 do > if type(i,safeprime) then printf("%d, ",i); end if; > end do; 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479,

> # Sophie Germain Prime: - Reference: http://oeis.org/A005384 > # 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559 > for i from 0 to 641 by 1 do > if type(i,sophiegermainprime) then printf("%d, ",i); end if; > end do; 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641,

> # Star Prime: - Reference: http://oeis.org/A083577 > # 13, 37, 73, 181, 337, 433, 541, 661, 937, 1093, 2053, 2281, 2521, 3037, 3313, 5581, 5953, 6337, 6733, 7561, 7993, 8893, 10333, 10837, 11353, 12421, 12973, 13537, 15913, 18481, 20533, 21961, 25741, 27337, 32413, 33301, 36037, 36973, 42841 > for i from 0 to 1093 by 1 do > if type(i,starprime) then printf("%d, ",i); end if; > end do; 13, 37, 73, 181, 337, 433, 541, 661, 937, 1093,

> # Thabit Prime: - Reference: http://oeis.org/A007505 > # 2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407, 59421121885698253195157962751, 30423614405477505635920876929023 (3)

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> for i from 0 to 383 by 1 do > if type(i,thabitprime) then printf("%d, ",i); end if; > end do; 2, 5, 11, 23, 47, 191, 383,

> # Wagstaff Form of (2p + 1) / 3 Prime: - Reference: http://oeis. org/A000979 > # 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643 > for i from 0 to 2731 by 1 do > if type(i,wagstaffformprime) then printf("%d, ",i); end if; > end do; 3, 11, 43, 683, 2731,

> # Wagstaff Value p Prime: - Reference: http://oeis.org/A000978 > # 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321, 986191, 4031399 > for i from 0 to 701 by 1 do > if type(i,wagstaffvalueprime) then printf("%d, ",i); end if; > end do; 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701,

> # Wieferich base 2 prime: - Reference: http://oeis.org/A001220 > # 1093, 3511 > for i from 0 to 3511 by 1 do > if type(i,wieferichbase2prime) then printf("%d, ",i); end if; > end do; 1093, 3511,

> # Wieferich base 3 prime: - Reference: http://oeis.org/A014127 > # 11, 1006003 > if type(11,wieferichbase3prime) then printf("%d, ",11); end if; > if type(1006003,wieferichbase3prime) then printf("%d, ",1006003); end if; 11, 1006003,

> # Wieferich base 5 prime: - Reference: http://oeis.org/A123692 > # 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 > for i from 0 to 40487 by 1 do > if type(i,wieferichbase5prime) then printf("%d, ",i); end if; > end do; (3)

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2, 20771, 40487,

> # Wieferich base 6 prime: - Reference: http://en.wikipedia. org/wiki/List_of_prime_numbers > # 66161, 534851, 3152573 > if type(66161,wieferichbase6prime) then printf("%d, ",66161); end if; > if type(534851,wieferichbase6prime) then printf("%d, ",534851); end if; > if type(3152573,wieferichbase6prime) then printf("%d, ",3152573); end if; 66161, 534851, 3152573,

> # Wieferich base 7 prime: - Reference: http://oeis.org/A123693 > # 5, 491531 > if type(5,wieferichbase7prime) then printf("%d, ",5); end if; > if type(491531,wieferichbase7prime) then printf("%d, ",491531); end if; 5, 491531,

> # Wieferich base 10 prime: - Reference: http://oeis.org/A045616 > # 3, 487, 56598313 > for i from 0 to 487 by 1 do > if type(i,wieferichbase10prime) then printf("%d, ",i); end if; > end do; 3, 487,

> # Wieferich base 11 prime: - Reference: http://en.wikipedia. org/wiki/List_of_prime_numbers > # 71 > for i from 0 to 71 by 1 do > if type(i,wieferichbase11prime) then printf("%d, ",i); end if; > end do; 71,

> # Wieferich base 12 prime: - Reference: http://oeis.org/A111027 > # 2693, 123653 > if type(2693,wieferichbase12prime) then printf("%d, ",2693); end if; > if type(123653,wieferichbase12prime) then printf("%d, ",123653); end if; 2693, 123653, (3)

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> # Wieferich base 13 prime: - Reference: http://oeis.org/A128667 > # 2, 863, 1747591 > for i from 0 to 863 by 1 do > if type(i,wieferichbase13prime) then printf("%d, ",i); end if; > end do; 2, 863,

> # Wieferich base 17 prime: - Reference: http://en.wikipedia. org/wiki/List_of_prime_numbers > # 2, 3, 46021, 48947 > for i from 0 to 48947 by 1 do > if type(i,wieferichbase17prime) then printf("%d, ",i); end if; > end do; 2, 3, 46021, 48947,

> # Wieferich base 19 prime: - Reference: http://oeis.org/A090968 > # 3, 7, 13, 43, 137, 63061489 > for i from 0 to 137 by 1 do > if type(i,wieferichbase19prime) then printf("%d, ",i); end if; > end do; 3, 7, 13, 43, 137, (3)

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> # Michael Carter, Computer Scientist and Software Developer