This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331083 #10 Jan 09 2020 03:06:13
%S A331083 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,
%T A331083 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,
%U A331083 3,3,4,4,3,4,4,5,4,3,4,3,2,3,3,4,3,2,3
%N A331083 The number of terms in the negaFibonacci representation of n (A215022).
%C A331083 The Fibonacci numbers F(2*n) are the indices of records of this sequence.
%H A331083 Amiram Eldar, <a href="/A331083/b331083.txt">Table of n, a(n) for n = 1..10000</a>
%F A331083 a(A000045(2*n - 1)) = 1.
%F A331083 a(A000045(2*n)) = n.
%e A331083 The negaFibonacci representation of 3 is A215022(3) = 101, thus a(3) = 1 + 0 + 1 = 2.
%t A331083 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]
%Y A331083 Cf. A000045, A215022, A331084.
%Y A331083 Cf. A000120, A007895, A007953, A053735, A095791.
%K A331083 nonn,base
%O A331083 1,3
%A A331083 _Amiram Eldar_, Jan 08 2020