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A164642 Numbers n such that n, n + 4 and n + 6 are prime powers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

CROSSREFS

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

Sequence in context: A219674 A075571 A077133 * A247633 A277717 A120460

Adjacent sequences:  A164639 A164640 A164641 * A164643 A164644 A164645

KEYWORD

nonn

AUTHOR

Daniel Forgues, Aug 18 2009

STATUS

approved

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Last modified December 7 14:52 EST 2016. Contains 278877 sequences.