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A258242 Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A022838 (the Beatty sequence for sqrt(3)) and x -> [r*x] otherwise, where [ ] = floor and r = sqrt(3). 3
0, 1, 3, 2, 4, 4, 3, 5, 5, 7, 5, 7, 4, 6, 8, 6, 8, 8, 10, 6, 8, 10, 5, 7, 7, 9, 11, 7, 9, 9, 11, 9, 11, 13, 7, 9, 9, 11, 11, 6, 8, 8, 10, 8, 10, 10, 12, 14, 8, 10, 10, 10, 12, 12, 14, 10, 12, 12, 14, 16, 8, 10, 10, 12, 10, 12, 14, 12, 14, 7, 9, 9, 9, 11, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = number of edges from 0 to n in the tree at A258241.

LINKS

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

EXAMPLE

16->27->15->8->4->6->3->1->0, so that a(16) = 8.

MATHEMATICA

r = Sqrt[3]; 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. A022838, A258241, A258212.

Sequence in context: A110550 A236333 A128220 * A287869 A134749 A061901

Adjacent sequences:  A258239 A258240 A258241 * A258243 A258244 A258245

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 07 2015

STATUS

approved

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Last modified December 9 08:06 EST 2021. Contains 349627 sequences. (Running on oeis4.)