OFFSET
1,2
COMMENTS
Numbers n such that n + (0, 4, 6) is a prime power triple.
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.
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 *)
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Forgues, Aug 18 2009
STATUS
approved