A260678 Numbers n>0 for which n+(17-n)^2 is not prime.

33, 34, 37, 42, 49, 50, 51, 53, 56, 58, 60, 65, 67, 68, 69, 71, 72, 75, 78, 82, 83, 84, 85, 86, 88, 91, 94, 95, 97, 100, 101, 102, 105, 106, 107, 110, 111, 113, 114, 116, 117, 118, 119, 122, 123, 124, 128, 129, 132, 133, 134, 135, 136, 139, 141, 143, 148, 151, 152, 153

Offset

1,1

Comments

Motivated by the fact that n+(17-n)^2 = 1+16^2, 2+15^2, ..., 16+1^2, 17+0^2, 18+1^2, 19+2^2, ..., 32+15^2 are all prime. This has an explanation through Heegener numbers, similar to Euler's prime-generating polynomial, cf. A002837 and related crossrefs.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

remove(t -> isprime(t+(17-t)^2), [$1..200]); # Robert Israel, May 02 2017

Mathematica

Select[Range[200], !PrimeQ[# + (17 - #)^2] &] (* Vincenzo Librandi, Nov 16 2015 *)

Prog

(PARI) for(n=1, 999, isprime(n+(17-n)^2)||print1(n", "))
(Magma) [n: n in [1..180] | not IsPrime(n+(17-n)^2)]; // Vincenzo Librandi, Nov 16 2015

Crossrefs

Cf. A260679 (n+(17-n)^2), A007635 (primes in that sequence = primes of the form n^2+n+17).

Cf. A002837 (n^2-n+41 is prime), A005846 (primes of form n^2+n+41), A007634 (n^2+n+41 is composite), A097823 (n^2+n+41 is not squarefree).

Sequence in context: A115394 A344143 A335072 * A329658 A344139 A140143

Adjacent sequences: A260675 A260676 A260677 * A260679 A260680 A260681

Keyword

nonn,easy

Author

M. F. Hasler, Nov 15 2015

Status

approved