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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
OFFSET
0,2
COMMENTS
a(n) = number of edges from 0 to n in the tree at A258239.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2015
STATUS
approved