A164642 - OEIS

%I #14 Feb 22 2020 20:38:10

%S 1,3,5,7,13,19,23,25,37,43,67,97,103,121,163,193,223,277,307,343,457,

%T 613,823,853,877,1087,1297,1423,1447,1483,1663,1693,1783,1867,1873,

%U 1993,2083,2137,2203,2377,2683,2707,2797,3163,3253,3457,3463,3847,4153,4513

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

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

%C 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.

%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 Harvey P. Dale, <a href="/A164642/b164642.txt">Table of n, a(n) for n = 1..1000</a> (* first 272 terms from Daniel Forgues *)

%t ppQ[n_]:=Length/@FactorInteger[{n,n+4,n+6}]=={1,1,1}; Select[ Range[ 5000],ppQ] (* _Harvey P. Dale_, Jul 10 2016 *)

%t 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 *)

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

%K nonn

%O 1,2

%A _Daniel Forgues_, Aug 18 2009