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A113472
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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.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Prime gaps resulting from A113451.
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FORMULA
| a(n) = prime(A113451(n)+1) - prime(A113451(n)).
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EXAMPLE
| 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).
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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);
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MATHEMATICA
| f[n_] := GCD @@ Last /@ FactorInteger[n] != 1; Select[Table[Prime[n + 1] - Prime[n], {n, 350}], f] (*Chandler*)
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CROSSREFS
| Cf. A000040, A001597, A113451.
Sequence in context: A080678 A096300 A035672 * A105682 A049109 A035651
Adjacent sequences: A113469 A113470 A113471 * A113473 A113474 A113475
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KEYWORD
| easy,nonn
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AUTHOR
| Walter A. Kehowski (wkehowski(AT)cox.net), Jan 08 2006
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EXTENSIONS
| Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 19 2006
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