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 A226213 #8 Jun 13 2025 21:42:24
%S A226213 1,1,2,5,7,7,6,7,12,14,17,12,17,22,20,25,25,28,30,31,33,31,36,34,39,
%T A226213 39,32,42,45,42,48,45,51,51,43,54,57,55,60,52,63,63,60,66,63,70,72,67,
%U A226213 75,70,78,79,81,82,84,82,87,83,88,86,91,94,88,97,89,100
%N A226213 Zeckendorf distance between n and 2^n.
%C A226213 Zeckendorf distance is defined at A226207.
%H A226213 Clark Kimberling, <a href="/A226213/b226213.txt">Table of n, a(n) for n = 1..1000</a>
%e A226213 6 = 5 + 1 -> 3, and 2^6 = 55 + 8 + 1 -> 34 + 5 -> 21 + 3 -> 13 + 2 -> 8 + 1 -> 5 -> 3. The total number of Zeckendorf downshifts (i.e., arrows) is 7, so that a(6) = D(6,64) = 7.
%t A226213 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 A226213 lst = Map[d[#, 2^#] &, Range[100]] (* _Peter J. C. Moses_, May 30 2013 *)
%Y A226213 Cf. A226080, A226207.
%K A226213 nonn,easy
%O A226213 1,3
%A A226213 _Clark Kimberling_, May 31 2013