

A226212


Zeckendorf distance between n and floor(n/2).


3



1, 1, 2, 1, 2, 1, 3, 4, 4, 3, 5, 5, 4, 6, 6, 5, 5, 7, 7, 7, 6, 8, 8, 8, 8, 7, 7, 7, 9, 9, 9, 9, 9, 8, 8, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET

1,3


COMMENTS

Zeckendorf distance is defined at A226207.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000


EXAMPLE

11 = 8 + 3 > 5 + 2 > 3 + 1 > 2, and 5 > 3 > 2. The total number of Zeckendorf downshifts (i.e., arrows) is 5, so that a(11) = D(11,5) = 5.


MATHEMATICA

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[#, Floor[#/2]] &, Range[100]] (* Peter J. C. Moses, May 30 2013 *)


CROSSREFS

Cf. A226080, A226207, A226211.
Sequence in context: A133117 A210850 A051276 * A233439 A256600 A137752
Adjacent sequences: A226209 A226210 A226211 * A226213 A226214 A226215


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, May 31 2013


STATUS

approved



