

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.


3



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
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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



