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 A226208 #7 Dec 04 2016 19:46:31 %S A226208 1,1,2,3,2,4,5,2,4,6,2,7,2,4,6,2,8,2,4,9,2,4,6,2,8,2,4,10,2,4,6,2,11, %T A226208 2,4,6,2,8,2,4,10,2,4,6,2,12,2,4,6,2,8,2,4,13,2,4,6,2,8,2,4,10,2,4,6, %U A226208 2,12,2,4,6,2,8,2,4,14,2,4,6,2,8,2,4,10 %N A226208 Zeckendorf distance between n and n+1. %C A226208 Zeckendorf distance is defined at A226207. %H A226208 Clark Kimberling, <a href="/A226208/b226208.txt">Table of n, a(n) for n = 1..1000</a> %e A226208 7 = 5 + 2 -> 3 + 1 -> 2, and 8 -> 5 -> 3 -> 2. The total number of Zeckendorf downshifts (i.e., arrows) is 5, so that a(7) = D(7,8) = 5. %t A226208 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)]; lst = Map[d[#, # + 1] &, Range[100]] (* _Peter J. C. Moses_, May 30 2013 *) %Y A226208 Cf. A226080. %K A226208 nonn,easy %O A226208 1,3 %A A226208 _Clark Kimberling_, May 31 2013