A Crossnumber Meta: Nose Functions

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A CROSSNUMBER META: NOSE FUNCTIONS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 NOSE FUNCTIONS: A CROSSNUMBER: PAGE 1/3 In the clues below, n represents the number being clued and k and m represent unspecified positive integers. In neither case is there a connection between these values in different clues. Across 1. the smallest conductor of an elliptic curve over the rational numbers 3. the sum of the first k Sophie Germain primes 8. (the number of primes between two consecutive powers of 2) + (the floor of (k=e)k=e) 10. a divisor of 99999999 11. an even non-totient number 12. (a tribonacci number) + (the number of conjugacy classes in GL8(F2)) 13. 2n contains no zeros 14. (the average of the divisors of n is itself a divisor of n) + (a semiprime tribonacci number) 15. a palindrome with exactly 5 palindromic prime factors (counted with multiplicity) 16. a sum of four consecutive cubes 17. the kissing number in dimension 4 19. the number of permutations of length k with exactly 2 distinct cycle lengths (e.g. any transposition) 21. a palindromic even semiprime not expressible as the sum of two squares 22. a repdigit in base 10 that is also a repdigit when expressed in some smaller base larger than 1. Down 1. (a Sophie Germain prime equal to the sum of the first k Sophie Germain primes) · (the number of directed graphs with m unlabeled vertices and no self-loops or multiple edges in the same direction) 2. (a double factorial) + (``I'm a teapot'') 4. (a prime of the form p2 + q + 1 for consecutive primes p; q) · (a sum of seven consecutive squares) · (a safe prime) 5. (the smallest n > 2 so that all positive integers up to the hitchhiker number are squares modulo n) − (a prime of the form 2k + k3) NOSE FUNCTIONS: A CROSSNUMBER: PAGE 2/3 6. (a centered dodecahedral number) + (a positive cube) 7. an entry of the sequence defined by ak = 3ak−1 + 5 and a0 = 1 9. n + φ(n) is a power of 10 12. a Kaprekar number 18. n! + 1 is prime 20. a prime n containing 22-across, where 2 is a square modulo n NOSE FUNCTIONS: A CROSSNUMBER: PAGE 3/3.

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Input for Carnival of Math: Number 115, October 2014
Input for Carnival of Math: Number 115, October 2014 I visited Singapore in 1996 and the people were very kind to me. So I though this might be a little payback for their kindness. Good Luck. David Brooks The “Mathematical Association of America” (http://maanumberaday.blogspot.com/2009/11/115.html ) notes that: 115 = 5 x 23. 115 = 23 x (2 + 3). 115 has a unique representation as a sum of three squares: 3 2 + 5 2 + 9 2 = 115. 115 is the smallest three-digit integer, abc , such that ( abc )/( a*b*c) is prime : 115/5 = 23. STS-115 was a space shuttle mission to the International Space Station flown by the space shuttle Atlantis on Sept. 9, 2006. The “Online Encyclopedia of Integer Sequences” (http://www.oeis.org) notes that 115 is a tridecagonal (or 13-gonal) number. Also, 115 is the number of rooted trees with 8 vertices (or nodes). If you do a search for 115 on the OEIS website you will find out that there are 7,041 integer sequences that contain the number 115. The website “Positive Integers” (http://www.positiveintegers.org/115) notes that 115 is a palindromic and repdigit number when written in base 22 (5522). The website “Number Gossip” (http://www.numbergossip.com) notes that: 115 is the smallest three-digit integer, abc, such that (abc)/(a*b*c) is prime. It also notes that 115 is a composite, deficient, lucky, odd odious and square-free number. The website “Numbers Aplenty” (http://www.numbersaplenty.com/115) notes that: It has 4 divisors, whose sum is σ = 144.
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