A182649 Algorithm: x->[rx] if x even, x->[rx-x] if x odd, where r = (1+sqrt(5))/2, []=floor; a(n) is the number of steps from x=n to 0.

1, 3, 2, 6, 3, 5, 7, 9, 4, 8, 6, 8, 10, 12, 5, 7, 9, 11, 7, 11, 9, 11, 13, 15, 6, 10, 8, 10, 10, 14, 8, 10, 12, 14, 10, 14, 12, 14, 16, 18, 7, 9, 11, 13, 9, 13, 11, 13, 15, 17, 9, 13, 11, 13, 13, 17, 11, 13, 15, 17, 13, 17, 15, 17, 19, 21, 8, 12, 10

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

8->12->19->11->6->9->5->3->1->0; 9 steps, so that a(8) = 9.

Mathematica

r = GoldenRatio; f[x_] := If[OddQ[x], Floor[x/r], Floor[r*x]];
h[x_] := -1 + Length[Drop[FixedPointList[f, x], -1]];
Table[h[n], {n, 1, 100}] (* Clark Kimberling, May 04 2015 *)

Crossrefs

Cf. A182650, A182651, A182652.

Sequence in context: A186204 A137324 A011209 * A257698 A364384 A322907

Adjacent sequences: A182646 A182647 A182648 * A182650 A182651 A182652

Keyword

nonn

Author

Clark Kimberling, Nov 26 2010

Status

approved