

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
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OFFSET

0,2


COMMENTS

a(n) = number of edges from 0 to n in the tree at A258243.


LINKS

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


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

Cf. A022843, A258243, A258212.
Sequence in context: A209158 A209135 A258236 * A258248 A209139 A257161
Adjacent sequences: A258241 A258242 A258243 * A258245 A258246 A258247


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 08 2015


STATUS

approved



