A210363 Prime numbers p such that x^2 + x + p produces primes for x = 0..4 but not x = 5.

347, 641, 1427, 2687, 4001, 4637, 4931, 19421, 21011, 22271, 23741, 26711, 27941, 32057, 43781, 45821, 55331, 55817, 68207, 71327, 91571, 128657, 165701, 167621, 172421, 179897, 191447, 193871, 205421, 234191, 239231, 258107, 258611, 259157, 278807, 290021

Offset: 1

Author

T. D. Noe, Apr 05 2012

Keywords

• nonn

Comments

The first term is A164926(5).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067774, A164926, A210360, A210361, A210362, A210364, A210365.

Programs

Mathematica

lookfor = 5; t = {}; n = 0; While[Length[t] < 50, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t
Select[Prime[Range[26000]],AllTrue[#+{2,6,12,20},PrimeQ] && !PrimeQ[ #+30]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 13 2017 *)
Select[Prime[Range[26000]],Boole[PrimeQ[#+{2,6,12,20,30}]]=={1,1,1,1,0}&] (* Harvey P. Dale, May 29 2025 *)