A257702 Number of steps from n to 0 using this algorithm: x -> floor(r*x) if x is odd, and x -> floor(x/r) if x is even, where r = sqrt(5).

2, 1, 3, 3, 7, 2, 12, 4, 6, 4, 6, 8, 12, 3, 11, 13, 15, 5, 7, 5, 7, 7, 11, 5, 9, 7, 9, 9, 11, 13, 17, 4, 10, 12, 14, 14, 16, 14, 18, 16, 24, 6, 8, 8, 10, 6, 10, 8, 16, 8, 10, 12, 14, 6, 8, 10, 16, 10, 14, 8, 10, 10, 12, 10, 14, 12, 18, 14, 16, 18, 20, 5, 9

Offset: 1

Author

Clark Kimberling, May 04 2015

Keywords

• nonn
• easy

Examples

			5->11->24->10->4->1->2->0, total of 7 steps, so that a(5) = 7.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A257698-A257701, A257703-A257706.

Programs

Mathematica

r = Sqrt[5]; f[x_] := If[OddQ[x], Floor[r *x], Floor[x/r]]
g[x_] := Drop[FixedPointList[f, x], -1];
Table[-1 + Length[g[n]], {n, 1, 200}]