A258248 Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A022842 (the Beatty sequence for sqrt(8)) and x -> [r*x] otherwise, where r = sqrt(8) and [ ] = floor.

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

Offset

0,2

Comments

a(n) = number of edges from 0 to n in the tree at A258247.

Links

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

Example

13->36->12->33->11->3->8->2->0, so that a(12) = 8.

Mathematica

r = Sqrt[8]; 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. A022842, A258247, A258212.

Sequence in context: A209135 A258236 A258244 * A209139 A257161 A253676

Adjacent sequences: A258245 A258246 A258247 * A258249 A258250 A258251

Keyword

nonn,easy

Author

Clark Kimberling, Jun 08 2015

Status

approved