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Search: id:A117896
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| A117896 |
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Number of perfect powers between consecutive squares n^2 and (n+1)^2. |
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+0
2
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| 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n)=2 only 14 times for n<2^63. What is the least n such that a(n)=3? Is a(n) bounded?
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EXAMPLE
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a(5)=2 because powers 27 and 32 are between 25 and 36.
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MATHEMATICA
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nMax=150^2; lst={}; log2Max=Ceiling[Log[2, nMax]]; bases=Table[2, {log2Max}]; powers=bases^Range[log2Max]; powers[[1]]=Infinity; cnt=0; While[nextPP=Min[powers]; nextPP <= nMax, pos=Flatten[Position[powers, nextPP]]; If[MemberQ[pos, 2], AppendTo[lst, cnt]; cnt=0, cnt++ ]; Do[k=pos[[i]]; bases[[k]]++; powers[[k]]=bases[[k]]^k, {i, Length[pos]}]]; lst
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CROSSREFS
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Cf. A001597 (perfect powers), A014085 (primes between squares).
Sequence in context: A045837 A126825 A045833 this_sequence A132976 A143840 A028649
Adjacent sequences: A117893 A117894 A117895 this_sequence A117897 A117898 A117899
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 31 2006
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