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 A131343 #13 Feb 17 2022 09:59:22
%S A131343 0,1,1,2,2,2,3,3,3,3,4,3,3,4,4,4,4,5,4,4,4,5,4,4,5,5,5,5,6,4,4,5,5,5,
%T A131343 5,6,5,5,5,6,5,5,6,6,6,6,7,5,5,5,6,5,5,6,6,6,6,7,5,5,6,6,6,6,7,6,6,6,
%U A131343 7,6,6,7,7,7,7,8,5,5,6,6,6,6,7,6,6,6,7
%N A131343 Number of 1's in maximal Lucas representation (A130311) of n.
%H A131343 Amiram Eldar, <a href="/A131343/b131343.txt">Table of n, a(n) for n = 0..10000</a>
%H A131343 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>.
%F A131343 a(n) = A007953(A130311(n)). - _Amiram Eldar_, Feb 17 2022
%t A131343 lazy = Select[IntegerDigits[Range[400], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse@LucasL[Range[0, Length[#] - 1]]] & /@ lazy; Join[{0}, Plus@@@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]] (* _Amiram Eldar_, Feb 17 2022 *)
%Y A131343 Cf. A000032, A007895, A130311, A116543.
%K A131343 nonn,base
%O A131343 0,4
%A A131343 _Casey Mongoven_, Jun 29 2007
%E A131343 a(0) and more terms from _Amiram Eldar_, Feb 17 2022