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 A131340 #9 Jul 05 2025 09:40:51
%S A131340 1,0,2,3,2,2,4,3,3,3,5,4,4,4,4,3,3,6,5,5,5,5,4,4,5,4,4,4,7,6,6,6,6,5,
%T A131340 5,6,5,5,5,6,5,5,5,5,4,4,8,7,7,7,7,6,6,7,6,6,6,7,6,6,6,6,5,5,7,6,6,6,
%U A131340 6,5,5,6,5,5,5,9,8,8,8,8,7,7,8,7,7,7,8
%N A131340 Number of 0's in minimal Lucas representation (A130310) of n.
%H A131340 Amiram Eldar, <a href="/A131340/b131340.txt">Table of n, a(n) for n = 1..10000</a>
%H A131340 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html">Using the Fibonacci numbers to represent whole numbers</a>.
%t A131340 a[n_] := Module[{s = {}, m = n, k = 1}, While[m > 0, If[m == 1, k = 1; AppendTo[s, k]; m = 0, If[m == 2, k = 0; AppendTo[s, k]; m = 0, While[LucasL[k] <= m, k++]; k--; AppendTo[s, k]; m -= LucasL[k]; k = 1]]]; Total[1 - IntegerDigits[Total[2^s], 2]]]; Array[a, 100] (* _Amiram Eldar_, Jul 05 2025 *)
%Y A131340 Cf. A131341, A000032, A102364.
%K A131340 nonn
%O A131340 1,3
%A A131340 _Casey Mongoven_, Jun 29 2007
%E A131340 More terms from _Amiram Eldar_, Jul 05 2025