A253718 Number h such that (h,0) is n steps from (0,0), where steps are as follows: (x,y)->(x-r, y) if r > 0, and (x,y)->(y, r/3) otherwise, where r = x mod 3.

0, 1, 1, 3, 4, 4, 3, 4, 4, 5, 6, 6, 6, 7, 7, 6, 7, 7, 5, 6, 6, 6, 7, 7, 6, 7, 7, 7, 8, 8, 8, 9, 9, 8, 9, 9, 8, 9, 9, 9, 10, 10, 9, 10, 10, 8, 9, 9, 9, 10, 10, 9, 10, 10, 7, 8, 8, 8, 9, 9, 8, 9, 9, 8, 9, 9, 9, 10, 10, 9, 10, 10, 8, 9, 9, 9, 10, 10, 9, 10, 10

Offset: 0

Author

Clark Kimberling, May 02 2015

Keywords

• nonn
• easy

Comments

This is column 1 of the array at A253281.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A253281.

Programs

Mathematica

f[{x_, y_}] := If[IntegerQ[x/3], {y, x/3}, {x - Mod[x, 3], y}];
g[{x_, y_}] := Drop[FixedPointList[f, {x, y}], -1];
Table[-1 + Length[g[{n, 0}]], {n, 0, 200}]  (* A253718 *)