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 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. 3

%I

%S 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,

%T 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,

%U 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

%N 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.

%C Prime gaps resulting from A113451.

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

%e a(90) = prime(296)-prime(295) = 1949-1933 = 16 = 2^4.

%e a(329) = prime(1184)-prime(1183) = 9587-9551 = 36 = 6^2 (first term not a power of 2).

%p 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);

%t f[n_] := GCD @@ Last /@ FactorInteger[n] != 1; Select[Table[Prime[n + 1] - Prime[n], {n, 350}], f] (*Chandler*)

%Y Cf. A000040, A001597, A113451.

%K easy,nonn

%O 1,2

%A _Walter Kehowski_, Jan 08 2006

%E Edited and extended by _Ray Chandler_, Oct 19 2006

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