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A074332
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Direction from n-th perfect power to closest prime (-1 if down, 1 if up, 0 if two primes are closest).
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0
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-1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, -1, -1, 1, 0, 1, -1, 1, 0, 1, -1, -1, 0, -1, 1, -1, 0, -1, 1, 1, -1, 0, -1, 1, -1, 1, -1, -1, 1, 1, 0, 1, 1, -1, 1, 1, -1, -1, -1, 0, 0, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 0, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 0, 1, -1, 1, 0, -1, -1, -1, 1, 1, -1, 1, 1, 0, -1, -1, 1, -1, 1, 1, 0, -1, 1, -1, 1, 1, 1, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Sign(n-th perfect power - closest prime) or 0 if two primes are closest.
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EXAMPLE
| The 7th perfect power (A001597) is 27. The closest prime to 27 is 29. sign(27-29)=-1, so a(7)=-1. The 11th perfect power is 64. There is no single closest prime to 64, since two primes are closest, namely 61 and 67, so a(11)=0.
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MATHEMATICA
| NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; pp = Select[ Range[10000], !PrimeQ[ # ] && Apply[ GCD, Last[ Transpose[FactorInteger[ # ]]]] > 1 & ]; Join[{-1}, Sign[ Table[ NextPrim[pp[[n]]] - pp[[n]], {n, 1, 124}] - Table[ pp[[n]] - PrevPrim[pp[[n]]], {n, 1, 124}]]]
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CROSSREFS
| Cf. A001597.
Sequence in context: A094934 A054354 A156728 * A152065 A113428 A133101
Adjacent sequences: A074329 A074330 A074331 * A074333 A074334 A074335
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KEYWORD
| sign
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AUTHOR
| N. Fernandez (primeness(AT)borve.org), Oct 12 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 13 2002
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