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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 (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 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

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Last modified August 2 12:47 EDT 2021. Contains 346424 sequences. (Running on oeis4.)