

A164641


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


2



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
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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 nonadmissible pattern for prime triples, since (0, 2, 4) = (0, 0, 0) (mod 2) = (0, 2, 1) (mod 3), has low density.


LINKS



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.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



