A269721 Integers k such that k, k+2, k+4 and k+6 are prime powers (A000961).

1, 3, 5, 7, 23, 25

Offset

1,2

Comments

At least one of a(n), a(n)+2, a(n)+4 and a(n)+6 must be a power of 3. See comments in A264734.

Links

Table of n, a(n) for n=1..6.

Example

5 is a term because 5, 7, 11 are prime numbers and 9 = 3^2.
23 is a term because 23 and 29 are prime numbers and 25 = 5^2, 27 = 3^3.
25 is a term because 25 = 5^2, 27 = 3^3, 29 and 31 are prime numbers.

Mathematica

Select[Range[0, 10^5], AllTrue[Range[0, 6, 2] + #, Or[# == 1, PrimePowerQ@ #] &] &] (* Michael De Vlieger, Mar 04 2016, Version 10 *)

Prog

(PARI) lista(nn) = for(n=1, nn, if(n==1 || (isprimepower(n) && isprimepower(n+2) && isprimepower(n+4) && isprimepower(n+6)), print1(n, ", ")));

Crossrefs

Cf. A000961, A006549, A120431, A264734.

Sequence in context: A239282 A171015 A244571 * A084424 A137978 A155780

Adjacent sequences: A269718 A269719 A269720 * A269722 A269723 A269724

Keyword

nonn,more

Author

Altug Alkan, Mar 04 2016

Status

approved