A094786 Primes that are 2 less than a perfect power m^k, k >= 2.

2, 7, 23, 47, 79, 167, 223, 241, 359, 439, 727, 839, 1087, 1223, 1367, 1847, 2207, 2399, 3023, 3373, 3719, 3967, 4759, 5039, 5623, 5927, 6857, 7919, 8647, 10607, 11447, 13687, 14159, 14639, 16127, 17159, 18223, 19319, 19681, 21023, 24023, 25919

Offset: 1

Author

Cino Hilliard, Jun 10 2004

Keywords

• nonn
• changed

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001597 (perfect powers).

Programs

Mathematica

perfPQ[n_]:=GCD@@FactorInteger[n][[All,2]]>1; Select[Prime[Range[3000]],perfPQ[#+2]&] (* Harvey P. Dale, Aug 25 2025 *)

PARI

k(n,m) = forprime(x=2,n,if(ispower(x+m),print1(x","))) ispower(n) = { local(p,r,j); r = sqrt(n); for(j=2,floor(r), p = floor(log(n)/log(j)+.5); if(j^p ==n,return(1)); ); return(0) }

Extensions

Comment deleted by Zak Seidov, Apr 17 2013