A187057 Primes p such that the polynomial x^2 + x + p generates only primes for x = 0, ..., 4.

11, 17, 41, 347, 641, 1277, 1427, 1607, 2687, 3527, 4001, 4637, 4931, 13901, 19421, 21011, 21557, 22271, 23741, 26681, 26711, 27941, 28277, 31247, 32057, 33617, 43781, 45821, 55331, 55661, 55817, 68207, 68897, 71327, 91571, 97367, 113147, 128657, 128981

Offset

1,1

Comments

From Weber, p. 15.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

H. J. Weber, Regularities of Twin, Triplet and Multiplet Prime Numbers, Mar 2, 2011.

Example

a(1) = 11 because x^2 + x + 11 generates 0^2 + 0 + 11; 1^2 + 1 + 11 = 13; 2^2 + 2 + 11 = 17; 3^2 + 3 + 11 = 23; 4^2 + 4 + 11 = 31, all primes.

Mathematica

okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 4}]]; Select[Range[10000], okQ] (* T. D. Noe, Mar 03 2011 *)
Select[Prime[Range[12500]], AllTrue[#+{2, 6, 12, 20}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 11 2019 *)

Prog

(PARI) forprime(p=2, 1e4, if(isprime(p+2)&&isprime(p+6)&&isprime(p+12) &&isprime(p+20), print1(p", "))) \\ Charles R Greathouse IV, Mar 04 2012

Crossrefs

Sequence in context: A178070 A243222 A090609 * A187058 A144051 A331940

Adjacent sequences: A187054 A187055 A187056 * A187058 A187059 A187060

Keyword

nonn

Author

Jonathan Vos Post, Mar 03 2011

Status

approved