%I #12 Mar 07 2016 12:51:58

%S 1,3,5,7,23,25

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

%C 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.

%e 5 is a term because 5, 7, 11 are prime numbers and 9 = 3^2.

%e 23 is a term because 23 and 29 are prime numbers and 25 = 5^2, 27 = 3^3.

%e 25 is a term because 25 = 5^2, 27 = 3^3, 29 and 31 are prime numbers.

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

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

%Y Cf. A000961, A006549, A120431, A264734.

%K nonn,more

%O 1,2

%A _Altug Alkan_, Mar 04 2016