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Search: id:A113451
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| A113451 |
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Integers n such that prime(n+1)-prime(n) is a power. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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87 is in the sequence since prime(88)-prime(87) = 457-449 = 8 = 2^3.
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MAPLE
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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
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f[n_] := GCD @@ Last /@ FactorInteger[n] != 1; Select[Range[200], f[Prime[ # + 1] - Prime[ # ]] &] (*Chandler*)
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CROSSREFS
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Cf. A000040, A001597, A113472.
Sequence in context: A055670 A141096 A089257 this_sequence A029709 A046458 A096629
Adjacent sequences: A113448 A113449 A113450 this_sequence A113452 A113453 A113454
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KEYWORD
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easy,nonn
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AUTHOR
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Walter A. Kehowski (wkehowski(AT)cox.net), Jan 08 2006
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EXTENSIONS
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Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 19 2006
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