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A258236 Number of steps from n to 0, where allowable steps are x -> [x/r] if x is in upper Wythoff sequence (A001950) and x -> [r*x] otherwise, where [ ] = floor and r = (3+sqrt(5))/2. 3
0, 2, 1, 3, 5, 3, 5, 2, 4, 6, 4, 6, 8, 6, 8, 4, 6, 8, 6, 8, 3, 5, 7, 5, 7, 9, 7, 9, 5, 7, 9, 7, 9, 11, 9, 11, 7, 9, 11, 9, 11, 5, 7, 9, 7, 9, 11, 9, 11, 7, 9, 11, 9, 11, 4, 6, 8, 6, 8, 10, 8, 10, 6, 8, 10, 8, 10, 12, 10, 12, 8, 10, 12, 10, 12, 6, 8, 10, 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 A258235.

LINKS

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

EXAMPLE

29->75->28->10->3->7->2->0, so that a(29) = 7.

MATHEMATICA

r = GoldenRatio^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. A258235, A258212, A001950.

Sequence in context: A209152 A209158 A209135 * A258244 A258248 A209139

Adjacent sequences:  A258233 A258234 A258235 * A258237 A258238 A258239

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2015

STATUS

approved

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Last modified January 21 22:08 EST 2022. Contains 350480 sequences. (Running on oeis4.)