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 A226214 #8 Jun 13 2025 21:51:03
%S A226214 0,1,2,5,3,6,4,6,10,9,11,12,9,11,13,12,8,6,10,15,12,14,16,16,13,15,15,
%T A226214 11,17,11,13,18,18,15,17,17,19,19,19,16,16,18,18,18,14,14,8,12,14,16,
%U A226214 21,21,21,21,18,18,20,20,20,22,22,22,22,22,19,19,19,21
%N A226214 Zeckendorf distance between n and n^2.
%C A226214 Zeckendorf distance is defined at A226207.
%H A226214 Clark Kimberling, <a href="/A226214/b226214.txt">Table of n, a(n) for n = 1..1000</a>
%e A226214 7 = 5 + 2, and 7^2 = 34 + 13 + 2 -> 21 + 8 + 1 -> 13 + 5 -> 8 + 3 -> 5 + 2. The total number of Zeckendorf downshifts (i.e., arrows) is 4, so that a(7) = D(7,49) = 4.
%t A226214 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 A226214 lst = Map[d[#, #^2] &, Range[100]] (* _Peter J. C. Moses_, May 30 2013 *)
%Y A226214 Cf. A226080, A226207.
%K A226214 nonn,easy
%O A226214 1,3
%A A226214 _Clark Kimberling_, May 31 2013