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

Author

Clark Kimberling, Jun 05 2015

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A258212, A000201.

Programs

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}]