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 A226210 #11 Jun 13 2025 22:51:29
%S A226210 0,1,1,2,0,3,6,2,5,8,11,12,6,9,12,15,16,19,20,21,13,16,19,22,23,26,27,
%T A226210 28,31,32,33,34,35,25,28,31,34,35,38,39,40,43,44,45,46,47,50,51,52,53,
%U A226210 54,55,56,57,45,48,51,54,55,58,59,60,63,64,65,66,67,70
%N A226210 a(n) is the Zeckendorf distance between n and Fibonacci(n).
%C A226210 Zeckendorf distance is defined at A226207.
%H A226210 Clark Kimberling, <a href="/A226210/b226210.txt">Table of n, a(n) for n = 1..150</a>
%e A226210 7 = 5 + 2 -> 3 + 1 -> 2, and 13 -> 8 -> 5 -> 3 -> 2. The total number of Zeckendorf downshifts (i.e., arrows) is 6, so that a(7) = D(7,F(7)) = 6.
%t A226210 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 A226210 lst = Map[d[#, Fibonacci[#]] &, Range[100]] (* _Peter J. C. Moses_, May 30 2013 *)
%Y A226210 Cf. A226080, A226207, A000045.
%K A226210 nonn,easy
%O A226210 1,4
%A A226210 _Clark Kimberling_, May 31 2013