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 A331084 The number of terms in the negaFibonacci representation of -n (A215023). 3
 1, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 3, 4, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 2, 3, 4, 3, 3, 2, 3, 4, 3, 4, 5, 4, 4, 3, 4, 4, 3, 3, 2, 3, 4, 3, 4, 4, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 2, 3, 4, 3, 3, 2, 3, 4, 3, 4, 5, 4, 4, 3, 4, 4, 3, 3, 2, 3, 4, 3, 4, 5, 4, 4, 3, 4, 5, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Fibonacci numbers F(2*n - 1) are the indices of records of this sequence. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(A000045(2*n)) = 1. a(A000045(2*n - 1)) = n. EXAMPLE The negaFibonacci representation of 2 is A215023(2) = 1001, thus a(2) = 1 + 0 + 0 + 1 = 2. MATHEMATICA 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]; nf[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s]; a[n_] := nf[-n]; Array[a, 100] CROSSREFS Cf. A000045, A215023, A331083. Cf. A000120, A007895, A007953, A053735, A095791. Sequence in context: A123884 A178412 A182598 * A067694 A131810 A233519 Adjacent sequences:  A331081 A331082 A331083 * A331085 A331086 A331087 KEYWORD nonn,base AUTHOR Amiram Eldar, Jan 08 2020 STATUS approved

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Last modified June 5 09:58 EDT 2020. Contains 334840 sequences. (Running on oeis4.)