A182438 Numbers n such that neither n^2+n-1 nor n^2-n-1 is prime.

1, 18, 23, 33, 34, 37, 43, 52, 58, 62, 63, 72, 73, 74, 75, 78, 79, 80, 81, 82, 88, 91, 92, 98, 99, 105, 106, 107, 108, 109, 110, 111, 112, 113, 117, 118, 119, 122, 123, 124, 128, 129, 133, 136, 137, 143, 147, 151, 152, 157, 162, 166, 167, 168, 173

Offset: 1

Author

Alex Ratushnyak, Apr 28 2012

Keywords

• nonn
• easy

Examples

			18^2+18-1=341 is not prime, and 18^2-18-1=305 is not prime, so 18 is in the sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002328, A045546.

Programs

Magma

[n: n in [1..180] | not IsPrime(n^2+n-1) and not IsPrime(n^2-n-1)]; // Vincenzo Librandi, Jan 19 2013

Mathematica

Select[Range[500], !PrimeQ[#^2 + # - 1] && !PrimeQ[#^2 - # - 1] &] (* Vincenzo Librandi, Jan 19 2013 *)
Select[Range[200],NoneTrue[#^2+{#-1,-#-1},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 04 2018 *)

PARI

is(n)=!isprime(n^2+n-1) && !isprime(n^2-n-1) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) ~ n. - Charles R Greathouse IV, Jun 13 2017