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Search: id:A071532
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| A071532 |
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(-1) * Sum[ k =1,n, (-1)^floor((3/2)^k) ]. |
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+0
4
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| 1, 0, 1, 2, 3, 4, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 10, 9, 8, 9, 8, 9, 8, 7, 8, 7, 8, 9, 10, 11, 10, 9, 10, 9, 8, 7, 8, 7, 6, 7, 8, 7, 8, 7, 6, 5, 6, 7, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10, 11, 10, 11, 10, 9, 10, 9, 10, 9, 8, 7, 6, 5, 6, 7, 6, 7, 6, 5, 4, 5, 6, 5, 4, 5, 4, 3
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Let b(n) denote the number of k with 0<=k<=n such that floor((3/2)^k) = A002379(k) is even; then a(n) = n-2*b(n).
Equivalently: let c(n) denote the number of k, 0<=k<=n, such that floor((3/2)^k) = A002379(k) is odd, then a(n) = 2*c(n)-n.
Is a(n)>0? For n large enough does a(n)>sqrt(n) always hold?
Conjecture: asymptotically, a(n) ~ C * Log(n)^2 with C = 1.4.....
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LINKS
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Robert G. Wilson v, Graph of first 100000 terms
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FORMULA
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a(n) = (-1)*sum( i=1, n, (-1)^A002379 (i) )
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MATHEMATICA
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a[0] = 0; a[n_] := a[n] = a[n - 1] - (-1)^Floor[(3/2)^n]; Table[ a[n], {n, 0, 95}]
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PROGRAM
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(PARI) a(n)=-sum(i=1, n, sign((-1)^floor((3/2)^i)))
(PARI) a(n)=n-2*sum(k=0, n, if(floor((3/2)^k)%2, 0, 1))
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CROSSREFS
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Cf. A072418.
Sequence in context: A017861 A094700 A073635 this_sequence A102730 A165597 A099033
Adjacent sequences: A071529 A071530 A071531 this_sequence A071533 A071534 A071535
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 20 2002
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EXTENSIONS
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Edited by Ralf Stephan, Sep 01 2004
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