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A258240 Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A001952 (the Beatty sequence for 2 + sqrt(2)) and x -> [r*x] otherwise, where [ ] = floor and r = 2 + sqrt(2). 3
0, 2, 4, 1, 3, 5, 3, 5, 7, 9, 5, 7, 9, 2, 4, 6, 8, 4, 6, 8, 6, 8, 10, 4, 6, 8, 10, 6, 8, 10, 8, 10, 12, 14, 10, 12, 14, 6, 8, 10, 8, 10, 12, 14, 10, 12, 14, 3, 5, 7, 9, 5, 7, 9, 7, 9, 11, 13, 9, 11, 13, 5, 7, 9, 7, 9, 11, 13, 9, 11, 13, 7, 9, 11, 13, 9, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = number of edges from 0 to n in the tree at A258239.

LINKS

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

EXAMPLE

8->27->7->23->6->1->3->0, so that a(8) = 7.

MATHEMATICA

r = 2+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. A258239, A258212, A001952.

Sequence in context: A261595 A211197 A258246 * A198578 A173658 A277618

Adjacent sequences:  A258237 A258238 A258239 * A258241 A258242 A258243

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2015

STATUS

approved

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Last modified October 16 10:19 EDT 2021. Contains 348041 sequences. (Running on oeis4.)