A164641 Numbers n such that n, n + 2 and n + 6 are prime powers.

1, 2, 3, 5, 7, 11, 17, 23, 25, 41, 47, 101, 107, 125, 167, 191, 227, 311, 347, 461, 641, 727, 821, 857, 881, 1091, 1277, 1301, 1367, 1427, 1481, 1487, 1607, 1871, 1997, 2081, 2207, 2237, 2267, 2657, 2687, 3119, 3251, 3461, 3527, 3671, 3917, 4001, 4127, 4517

Offset

1,2

Comments

Numbers n such that n + (0, 2, 6) is a prime power triple.

Prime power triples with pattern n + (0, 2, 6), a generalization of the prime triples with pattern n + (0, 2, 6). The prime triples with pattern n + (0, 2, 6) are a subsequence.

n + (0, 2, 6), being an admissible pattern for prime triples, since (0, 2, 6) = (0, 0, 0) (mod 2) = (0, 2, 0) (mod 3), has high density.

n + (0, 4, 6), being an admissible pattern for prime triples, since (0, 4, 6) = (0, 0, 0) (mod 2) = (0, 1, 0) (mod 3), has high density.

n + (0, 2, 4), being a non-admissible pattern for prime triples, since (0, 2, 4) = (0, 0, 0) (mod 2) = (0, 2, 1) (mod 3), has low density.

Links

Daniel Forgues, Table of n, a(n) for n=1..279

Mathematica

Join[{1}, Select[Range[4600], AllTrue[#+{0, 2, 6}, PrimePowerQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 19 2020 *)

Crossrefs

Cf. A164642 Numbers n such that n, n+4 and n+6 are prime powers.

Sequence in context: A189828 A090481 A094342 * A058982 A040069 A057751

Adjacent sequences: A164638 A164639 A164640 * A164642 A164643 A164644

Keyword

nonn

Author

Daniel Forgues, Aug 18 2009

Extensions

Cross-reference corrected by Daniel Forgues, Oct 07 2009

Status

approved