A258246 Number of steps from n to 0, where allowable steps are x -> [x/Pi] if x = is in A022844 (the Beatty sequence for Pi) and x -> [Pi*x] otherwise, where [ ] = floor.

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

Offset: 0

Author

Clark Kimberling, Jun 08 2015

Keywords

• nonn
• easy

Comments

a(n) = number of edges from 0 to n in the tree at A258245.

Examples

			8->25->7->21->6->1->3->0, so that a(8) = 7.
		

Links

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

Crossrefs

Cf. A022844, A258245, A258212.

Programs

Mathematica

r = Pi; 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}]