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 A130310 #15 Feb 17 2022 08:02:06
%S A130310 0,10,1,100,1000,1010,1001,10000,10010,10001,10100,100000,100010,
%T A130310 100001,100100,101000,101010,101001,1000000,1000010,1000001,1000100,
%U A130310 1001000,1001010,1001001,1010000,1010010,1010001,1010100,10000000,10000010,10000001,10000100,10001000
%N A130310 Minimal (or "greedy") Lucas representation of n, in which L(0) = 2 and L(2) = 3 are not allowed in the same representation (hence the correct representation of the integer 5 is 1010 rather than 101). A binary system of integers with Lucas numbers (A000032) as a base.
%D A130310 Richard A. Dunlap, The Golden Ratio and Fibonacci Numbers, Singapore, World Scientific, 1997, pp. 73-77.
%D A130310 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 A130310 Amiram Eldar, <a href="/A130310/b130310.txt">Table of n, a(n) for n = 0..10000</a>
%H A130310 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phigits.html">Using Powers of Phi to represent Integers</a>.
%e A130310 a(9) = 10001 because 7 + 2 = 9.
%e A130310 a(10) is 10100 because 7 + 3 = 10.
%t A130310 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]]]; FromDigits @ IntegerDigits[Total[2^s], 2]]; Array[a, 30, 0] (* _Amiram Eldar_, Feb 17 2022 *)
%Y A130310 Cf. A000032, A014417, A116543, A130311.
%K A130310 nonn,base
%O A130310 0,2
%A A130310 _Casey Mongoven_, May 21 2007
%E A130310 Definition corrected by _Casey Mongoven_, May 29 2010
%E A130310 a(0) and more terms from _Amiram Eldar_, Feb 17 2022