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 A130311 #18 Feb 17 2022 09:59:56
%S A130311 0,10,1,11,110,101,111,1011,1110,1101,1111,10110,10101,10111,11011,
%T A130311 11110,11101,11111,101011,101110,101101,101111,110110,110101,110111,
%U A130311 111011,111110,111101,111111,1010110,1010101,1010111,1011011,1011110,1011101,1011111,1101011,1101110
%N A130311 Maximal (or "lazy") Lucas representation of n. Binary system for representing integers using Lucas numbers (A000032) as a base.
%D A130311 Edouard Zeckendorf, Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège, Vol. 41 (1972), pp. 179-182.
%H A130311 Amiram Eldar, <a href="/A130311/b130311.txt">Table of n, a(n) for n = 0..10000</a>
%H A130311 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html">Using Fibonacci Numbers to Represent Whole Numbers</a>.
%e A130311 a(7) = 1110 because 4 + 3 + 1 = 8.
%e A130311 a(8) = 1101 because 4 + 3 + 2 = 9.
%t A130311 lazy = Select[IntegerDigits[Range[10^2], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse@LucasL[Range[0, Length[#] - 1]]] & /@ lazy; Join[{0}, FromDigits /@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]] (* _Amiram Eldar_, Feb 17 2022 *)
%Y A130311 Cf. A000032, A104326, A130310, A131343.
%K A130311 nonn,base
%O A130311 0,2
%A A130311 _Casey Mongoven_, May 21 2007; corrected Mar 23 2008
%E A130311 a(0) and more terms from _Amiram Eldar_, Feb 17 2022