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 A226211 #8 Jun 13 2025 21:11:56
%S A226211 1,1,1,4,3,5,6,5,7,7,8,8,7,7,9,9,8,10,10,10,9,9,9,11,11,11,11,10,12,
%T A226211 12,12,12,12,11,11,11,11,13,13,13,13,13,13,13,12,12,14,14,14,14,14,14,
%U A226211 14,14,13,13,13,13,13,13,13,15,15,15,15,15,15,15,15,15
%N A226211 Zeckendorf distance between n and 2*n.
%C A226211 Zeckendorf distance is defined at A226207.
%H A226211 Clark Kimberling, <a href="/A226211/b226211.txt">Table of n, a(n) for n = 1..1000</a>
%e A226211 11 = 8 + 3 -> 5 + 2 -> 3 + 1 -> 2, and 22 = 21 + 1 -> 13 -> 8 -> 5 -> 3 -> 2. The total number of Zeckendorf downshifts (i.e., arrows) is 8, so that a(11) = D(11,22) = 8.
%t A226211 zeck[n_Integer] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, z = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[z, 1]; t = t - Fibonacci[k], AppendTo[z, 0]]; k--]; If[n > 0 && z[[1]] == 0, Rest[z], z]]; d[n1_, n2_] := Module[{z1 = zeck[n1], z2 = zeck[n2]}, Length[z1] + Length[z2] - 2 (NestWhile[# + 1 &, 1, z1[[#]] == z2[[#]] &, 1, Min[{Length[z1], Length[z2]}]] - 1)];
%t A226211 lst = Map[d[#, 2#] &, Range[100]] (* _Peter J. C. Moses_, May 30 2013 *)
%Y A226211 Cf. A226080, A226207, A226212.
%K A226211 nonn,easy
%O A226211 1,4
%A A226211 _Clark Kimberling_, May 31 2013