A247882 Numbers, p, that generate the prime quadruplets p^2-2p+2k (for k = -2, -1, 1, 2).

5, 15, 705, 2795, 14105, 18645, 38547, 43485, 53915, 57957, 62417, 76287, 82355, 94445, 96657, 145937, 162605, 178817, 180677, 184877, 193625, 234017, 238887, 256557, 261017, 287835, 297815, 334007, 339525, 346425, 387297, 399387, 407145, 417597, 418845, 419147

Offset

1,1

Comments

For a subset of this list, restricted only to primes, see A247845.

All terms == 5 or 7 (mod 10). - Robert Israel, Mar 10 2025

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

5 is in the sequence as it generates the prime quadruplet 5^2-2*5-4=11; 5^2-2*5-2=13; 5^2-2*5+2=17; and, 5^2-2*5+4=19.

Maple

filter:= p -> andmap(isprime, [p^2-2*p-4, p^2-2*p-2, p^2-2*p+2, p^2-2*p+4]):
select(filter, [seq(seq(10*i+j, j=[5, 7]), i=0..10^6)]);

Prog

(PARI) lista(nn) = {vk = [-2, -1, 1, 2]; for (p = 2, nn, nb = 0; for (k = 1, 4, nb += isprime(p^2-2*p+2*vk[k]); ); if (nb == 4, print1(p, ", ")); ); } \\ Michel Marcus, Sep 26 2014

Crossrefs

Cf. A247845 (subsequence of primes).

Sequence in context: A298510 A371887 A318898 * A215901 A112515 A001141

Adjacent sequences: A247879 A247880 A247881 * A247883 A247884 A247885

Keyword

nonn

Author

Ray G. Opao, Sep 25 2014

Extensions

More terms from Michel Marcus, Sep 26 2014

Status

approved