A113472 If d(n) is the sequence of prime differences prime(n+1) - prime(n), then a(n) is the subsequence of d(n) such that d(n) is a power.

1, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 8, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 4, 4, 4, 8, 8, 8, 4, 8, 4, 8, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 8, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 8, 4, 4, 8, 4, 4, 4, 8, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 16, 4, 4, 16, 8, 4, 4, 8, 4, 16, 4, 8, 4, 8, 16, 4, 8

Offset: 1

Author

Walter Kehowski, Jan 08 2006

Keywords

• easy
• nonn

Comments

Prime gaps resulting from A113451.

Examples

			a(90) = prime(296) - prime(295) = 1949 - 1933 = 16 = 2^4.
a(329) = prime(1184) - prime(1183) = 9587 - 9551 = 36 = 6^2 (first term not a power of 2).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A000040, A001597, A113451.

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[Table[Prime[n + 1] - Prime[n], {n, 350}], f] (* Ray Chandler, Oct 19 2006 *)

Formula

a(n) = prime(A113451(n)+1) - prime(A113451(n)).

Extensions

Edited and extended by Ray Chandler, Oct 19 2006