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A331083
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The number of terms in the negaFibonacci representation of n (A215022).
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5
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1, 1, 2, 2, 1, 2, 2, 3, 3, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 3, 4, 3, 2, 3, 3, 4, 4, 3, 4, 4, 5, 5, 4, 5, 4, 3, 4, 4, 5, 4, 3, 4, 3, 2, 3, 3, 4, 4, 3, 4, 4, 5, 4, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3
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OFFSET
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1,3
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COMMENTS
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The Fibonacci numbers F(2*n) are the indices of records of this sequence.
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LINKS
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FORMULA
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EXAMPLE
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The negaFibonacci representation of 3 is A215022(3) = 101, thus a(3) = 1 + 0 + 1 = 2.
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MATHEMATICA
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ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]]; f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i]; a[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s]; Array[a, 100]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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