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 A135818 #12 Jul 01 2023 09:19:47
%S A135818 1,0,1,2,0,3,1,1,4,2,2,2,0,5,3,3,3,1,3,1,1,6,4,4,4,2,4,2,2,4,2,2,2,0,
%T A135818 7,5,5,5,3,5,3,3,5,3,3,3,1,5,3,3,3,1,3,1,1,8,6,6,6,4,6,4,4,6,4,4,4,2,
%U A135818 6,4,4,4,2,4,2,2,6,4,4,4,2,4,2,2,4,2,2,2,0,9,7,7,7,5,7,5,5,7,5,5,5,3,7,5,5
%N A135818 Number of 1's (or A's) in the Wythoff representation of n.
%C A135818 a(n) = number of applications of Wythoff's A sequence A000201 needed in the unique Wythoff representation of n>=1.
%C A135818 See A135817 for references and links for the Wythoff representation for n>=1.
%H A135818 Amiram Eldar, <a href="/A135818/b135818.txt">Table of n, a(n) for n = 1..10000</a>
%e A135818 6 = A(A(A(B(1)))) = AAAB = `1110`, hence a(6)=3.
%t A135818 z[n_] := Floor[(n + 1)*GoldenRatio] - n - 1; h[n_] := z[n] - z[n - 1]; w[n_] := Module[{m = n, zm = 0, hm, s = {}}, While[zm != 1, hm = h[m]; AppendTo[s, hm]; If[hm == 1, zm = z[m], zm = z[z[m]]]; m = zm]; s]; w[0] = 0; a[n_] := Total[w[n]]; Array[a, 100] (* _Amiram Eldar_, Jul 01 2023 *)
%Y A135818 Cf. A000201, A135817 (lengths of Wythoff representation), A007895 (number of 0's (or B's) in the Wythoff representation).
%K A135818 nonn,base,easy
%O A135818 1,4
%A A135818 _Wolfdieter Lang_, Jan 21 2008