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A258244
Number of steps from n to 0, where allowable steps are x -> [x/e] if x = is in A022843 (the Beatty sequence for e) and x -> [e*x] otherwise, where [ ] = floor.
4
0, 2, 1, 3, 5, 3, 5, 7, 2, 4, 4, 6, 8, 6, 8, 10, 4, 6, 8, 6, 8, 8, 10, 12, 3, 5, 7, 5, 7, 5, 7, 9, 7, 9, 11, 9, 11, 13, 7, 9, 9, 11, 13, 11, 13, 15, 5, 7, 7, 9, 11, 9, 11, 13, 7, 9, 11, 9, 11, 9, 11, 13, 11, 13, 15, 13, 15, 4, 6, 8, 6, 8, 10, 8, 10, 12, 6, 8
OFFSET
0,2
COMMENTS
a(n) = number of edges from 0 to n in the tree at A258243.
LINKS
EXAMPLE
20->54->19->6->16->5->1->2->0, so that a(20) = 8.
MATHEMATICA
r = E; 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 08 2015
STATUS
approved