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%I #7 Aug 19 2020 16:30:40
%S 1,2,3,5,7,11,17,23,25,41,47,101,107,125,167,191,227,311,347,461,641,
%T 727,821,857,881,1091,1277,1301,1367,1427,1481,1487,1607,1871,1997,
%U 2081,2207,2237,2267,2657,2687,3119,3251,3461,3527,3671,3917,4001,4127,4517
%N Numbers n such that n, n + 2 and n + 6 are prime powers.
%C Numbers n such that n + (0, 2, 6) is a prime power triple.
%C 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.
%C 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.
%C 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.
%C 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.
%H Daniel Forgues, <a href="/A164641/b164641.txt">Table of n, a(n) for n=1..279</a>
%t 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 *)
%Y Cf. A164642 Numbers n such that n, n+4 and n+6 are prime powers.
%K nonn
%O 1,2
%A _Daniel Forgues_, Aug 18 2009
%E Cross-reference corrected by _Daniel Forgues_, Oct 07 2009
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