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A226213 Zeckendorf distance between n and 2^n. 2
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, 39, 32, 42, 45, 42, 48, 45, 51, 51, 43, 54, 57, 55, 60, 52, 63, 63, 60, 66, 63, 70, 72, 67, 75, 70, 78, 79, 81, 82, 84, 82, 87, 83, 88, 86, 91, 94, 88, 97, 89, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Zeckendorf distance is defined at A226207.
LINKS
EXAMPLE
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.
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[#, 2^#]] &, Range[100]] (* Peter J. C. Moses, May 30 2013 *)
CROSSREFS
Sequence in context: A021392 A373919 A131688 * A199590 A096624 A145378
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 31 2013
STATUS
approved

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Last modified July 18 15:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)