

A258238


Number of steps from n to 0, where allowable steps are x > [x/r] if x = is in A001951 (the Beatty sequence for sqrt(2)) and x > [r*x] otherwise, where [ ] = floor and r = sqrt(2).


3



0, 1, 2, 4, 3, 5, 7, 4, 6, 8, 10, 5, 7, 9, 9, 11, 6, 8, 8, 10, 12, 10, 12, 14, 7, 9, 9, 11, 11, 13, 15, 11, 13, 15, 17, 8, 10, 12, 10, 12, 14, 12, 14, 16, 18, 12, 14, 16, 16, 18, 9, 11, 11, 13, 15, 11, 13, 15, 17, 13, 15, 17, 17, 19, 21, 13, 15, 17, 19, 17
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OFFSET

0,3


COMMENTS

a(n) = number of edges from 0 to n in the tree at A258237.


LINKS

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


EXAMPLE

36>25>17>24>16>11>7>4>2>1>0, so that a(36) = 10.


MATHEMATICA

r = Sqrt[2]; 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. A258237, A258212, A001951.
Sequence in context: A210536 A102767 A336640 * A166266 A011295 A082016
Adjacent sequences: A258235 A258236 A258237 * A258239 A258240 A258241


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 05 2015


STATUS

approved



