A258215 Number of steps from n to 0, where allowable steps are x -> [x/r] if x is in lower Wythoff sequence (A000201) and x -> [r*x] otherwise, where [ ] = floor and r = (1+sqrt(5))/2 = golden ratio.

0, 1, 3, 2, 4, 6, 3, 5, 5, 7, 9, 4, 6, 8, 6, 8, 8, 10, 12, 5, 7, 7, 9, 11, 7, 9, 11, 9, 11, 11, 13, 15, 6, 8, 10, 8, 10, 10, 12, 14, 8, 10, 10, 12, 14, 10, 12, 14, 12, 14, 14, 16, 18, 7, 9, 9, 11, 13, 9, 11, 13, 11, 13, 13, 15, 17, 9, 11, 13, 11, 13, 13, 15

Offset

0,3

Comments

a(n) = number of edges from 0 to n in the tree at A258212.

Links

Clark Kimberling, Table of n, a(n) for n = 0..10000

Example

35->21->12->7->11->6->3->1->0, so that a(35) = 8.

Mathematica

r = GoldenRatio; w = Table[Floor[r*n], {n, 1, 1000}];
f[x_] := If[MemberQ[w, x], Floor[x/r], Floor[r*x]];
g[x_] := Drop[FixedPointList[f, x], -1];
Table[-1+ Length[g[n]], {n, 0, 100}]

Crossrefs

Cf. A258212, A000201.

Sequence in context: A280318 A353659 A246982 * A319073 A129601 A340579

Adjacent sequences: A258212 A258213 A258214 * A258216 A258217 A258218

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2015

Status

approved