A329364 Numbers k such that k, k+2, k+4 are prime powers.

1, 3, 5, 7, 9, 23, 25, 27, 79, 239, 59049, 450283905890997359, 36472996377170786399

Offset: 1

Author

Lior Manor, Nov 12 2019

Keywords

• nonn
• more

Comments

Intersection of A120431 and A164572.

a(14) > 10^3000, if it exists. Note that one among k, k+2, k+4 is always divisible by 3, so it must be a power of 3. - Giovanni Resta, Nov 12 2019

Examples

			7 is a term since 7, 9, and 11 are all prime powers.
		

Crossrefs

Cf. A001359, A000961, A120431, A164572.

Programs

Mathematica

pp[w_] := w == 1 || And @@ PrimePowerQ[w + {0,2,4}]; Reap[ Do[ If[pp[n - k], Sow[n-k]], {n, 3^Range[100]}, {k, {4, 2, 0}}]][[2, 1]] (* Giovanni Resta, Nov 12 2019 *)

PARI

isok(k) = (k==1) || (isprimepower(k) && isprimepower(k+2) && isprimepower(k+4)); \\ Michel Marcus, Nov 12 2019

Extensions

a(12)-a(13) from Giovanni Resta, Nov 12 2019