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A331083
The number of terms in the negaFibonacci representation of n (A215022).
5
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
OFFSET
1,3
COMMENTS
The Fibonacci numbers F(2*n) are the indices of records of this sequence.
LINKS
FORMULA
a(A000045(2*n - 1)) = 1.
a(A000045(2*n)) = n.
EXAMPLE
The negaFibonacci representation of 3 is A215022(3) = 101, thus a(3) = 1 + 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]; a[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s]; Array[a, 100]
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 08 2020
STATUS
approved