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Search: id:A074332
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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
1
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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; listen)
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OFFSET
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1,1
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FORMULA
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Sign(n-th perfect power - closest prime) or 0 if two primes are closest.
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EXAMPLE
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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
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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
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Cf. A001597.
Sequence in context: A054354 A156728 A071039 this_sequence A152065 A113428 A133101
Adjacent sequences: A074329 A074330 A074331 this_sequence A074333 A074334 A074335
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KEYWORD
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sign
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AUTHOR
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N. Fernandez (primeness(AT)borve.org), Oct 12 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 13 2002
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