A257701 Number of steps from n to 1 using this algorithm: x -> floor(r*x) if x is odd, and x -> floor(x/r) if x is even, where r = sqrt(3).

0, 1, 5, 2, 4, 6, 8, 3, 16, 5, 9, 7, 9, 4, 15, 17, 21, 6, 8, 10, 12, 8, 18, 10, 14, 16, 18, 18, 20, 22, 32, 7, 11, 9, 11, 11, 13, 13, 17, 19, 23, 11, 13, 15, 19, 17, 21, 19, 21, 19, 21, 23, 31, 33, 37, 8, 10, 12, 14, 10, 22, 12, 16, 12, 14, 14, 16, 18, 22

Offset

1,3

Links

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

Example

7->12->6->3->5->8->4->2->1, total of 8 steps, so that a(7) = 8.

Mathematica

r = Sqrt[3]; 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}]

Crossrefs

Cf. A257698-A257700, A257702-A257706.

Sequence in context: A308171 A265287 A329477 * A202494 A112597 A257700

Adjacent sequences: A257698 A257699 A257700 * A257702 A257703 A257704

Keyword

nonn,easy

Author

Clark Kimberling, May 04 2015

Status

approved