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A260678 Numbers n>0 for which n+(17-n)^2 is not prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A112817 A115394 A335072 * A329658 A140143 A041543

Adjacent sequences:  A260675 A260676 A260677 * A260679 A260680 A260681

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 15 2015

STATUS

approved

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Last modified August 7 09:16 EDT 2020. Contains 336274 sequences. (Running on oeis4.)