A113451 Integers n such that prime(n+1) - prime(n) is a power.

1, 4, 6, 8, 12, 14, 19, 22, 24, 25, 27, 29, 31, 38, 44, 48, 50, 59, 63, 65, 70, 72, 75, 77, 78, 79, 85, 87, 88, 90, 92, 93, 94, 95, 112, 117, 122, 124, 126, 128, 131, 132, 134, 135, 136, 143, 147, 149, 151, 153, 155, 156, 158, 159, 163, 166, 169, 181, 183, 186, 192, 196

Offset: 1

Author

Walter Kehowski, Jan 08 2006

Keywords

• easy
• nonn

Examples

			87 is in the sequence since prime(88) - prime(87) = 457 - 449 = 8 = 2^3.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000040, A001597, A113472.

Programs

Maple

egcd := proc(n) local L; L:=ifactors(n)[2]; L:=map(proc(z) z[2] end, L); igcd(op(L)) end; M:=[]: cnt:=0: for z to 1 do for k from 1 to 200 do p:=ithprime(k); q:=nextprime(p); x:=q-p; if egcd(x)>1 then cnt:=cnt+1; M:=[op(M), [cnt,k,x]] fi od od; M; map(proc(z) z[3] end, M);

Mathematica

f[n_] := GCD @@ Last /@ FactorInteger[n] != 1; Select[Range[200], f[Prime[ # + 1] - Prime[ # ]] &] (* Ray Chandler, Oct 19 2006 *)

Extensions

Edited by Ray Chandler, Oct 19 2006