A260679 -id:A260679 - cp's OEIS frontend

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

M. F. Hasler, Nov 15 2015

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.

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

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).

[n: n in [1..180] | not IsPrime(n+(17-n)^2)]; // Vincenzo Librandi, Nov 16 2015

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

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

for(n=1,999,isprime(n+(17-n)^2)||print1(n","))

cp's OEIS Frontend

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

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