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%I #16 Oct 01 2020 04:05:21
%S 1,2,3,5,7,11,13,17,19,23,25,31,37,41,43,47,53,61,67,73,83,97,101,103,
%T 107,121,125,131,151,157,163,167,173,191,193,223,227,233,251,257,263,
%U 271,277,283,307,311,331,337,343,347,353,361,367,373,383,433,443,457
%N Numbers k such that k and k+6 are both prime powers.
%C Numbers n such that n + (0, 6) is a prime power pair.
%C n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.
%C n + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, since (0, 2m-1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.]
%H Amiram Eldar, <a href="/A164574/b164574.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2492 from Daniel Forgues)
%t Join[{1},Select[Range[500],AllTrue[{#,#+6},PrimePowerQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 30 2018 *)
%o (PARI) is(n)=if(n<4,return(n>0)); isprimepower(n) && isprimepower(n+6) \\ _Charles R Greathouse IV_, Apr 24 2015
%Y Cf. A023201, A000961.
%Y k and (x) are prime powers: A006549 (k+1) A120431 (k+2), A164571 (k+3), A164572 (k+4), A164573 (k+5), this sequence (k+6).
%K nonn
%O 1,2
%A _Daniel Forgues_, Aug 16 2009
%E Edited by _Daniel Forgues_, Aug 17 2009
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