A331083 The number of terms in the negaFibonacci representation of n (A215022).

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

Author

Amiram Eldar, Jan 08 2020

Keywords

• nonn
• base

Comments

The Fibonacci numbers F(2*n) are the indices of records of this sequence.

Examples

			The negaFibonacci representation of 3 is A215022(3) = 101, thus a(3) = 1 + 0 + 1 = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A215022, A331084.

Cf. A000120, A007895, A007953, A053735, A095791.

Programs

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]

Formula

a(A000045(2*n - 1)) = 1.

a(A000045(2*n)) = n.