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

1, 3, 5, 7, 13, 19, 23, 25, 37, 43, 67, 97, 103, 121, 163, 193, 223, 277, 307, 343, 457, 613, 823, 853, 877, 1087, 1297, 1423, 1447, 1483, 1663, 1693, 1783, 1867, 1873, 1993, 2083, 2137, 2203, 2377, 2683, 2707, 2797, 3163, 3253, 3457, 3463, 3847, 4153, 4513

Offset

1,2

Comments

Numbers n such that n + (0, 4, 6) is a prime power triple.

Prime power triples with pattern n + (0, 4, 6), a generalization of the prime triples with pattern n + (0, 4, 6). The prime triples with pattern n + (0, 4, 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

Harvey P. Dale, Table of n, a(n) for n = 1..1000 (* first 272 terms from Daniel Forgues *)

Mathematica

ppQ[n_]:=Length/@FactorInteger[{n, n+4, n+6}]=={1, 1, 1}; Select[ Range[ 5000], ppQ] (* Harvey P. Dale, Jul 10 2016 *)
Join[{1}, SequencePosition[Table[If[PrimePowerQ[n], 1, 0], {n, 5000}], {1, _, _, _, 1, _, 1}][[All, 1]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 22 2020 *)

Crossrefs

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

Sequence in context: A219674 A075571 A077133 * A247633 A357170 A277717

Adjacent sequences: A164639 A164640 A164641 * A164643 A164644 A164645

Keyword

nonn

Author

Daniel Forgues, Aug 18 2009

Status

approved