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A167383
Entropy like stair step sequence based on A008185: a(n)=a(n-1)+Ceiling[ -(A008185[n + 2]/A008185[n + 1])*Log[(A008185[n + 2]/A008185[n + 1])]/Log[2]]
0
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22
OFFSET
0,15
COMMENTS
By using the ratio:
A008185[n + 2]/A008185[n + 1]
the sequence gets a probability effect that gives
a devil's staircase like result.
FORMULA
a(n)=a(n-1)+Ceiling[ -(A008185[n + 2]/A008185[n + 1])*Log[(A008185[n + 2]/A008185[n + 1])]/Log[2]]
MATHEMATICA
Clear[f, g, n]; f[0] = 1; f[1] = 1; f[2] = 1;
f[n_] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]];
g[0] = 0; g[1] = 1;
g[n_] := g[n] = g[n - 1] + Ceiling[ -(f[n + 2]/f[n + 1])*Log[(f[n + 2]/f[n + 1])]/Log[2]]
a = Table[g[n], {n, 0, 200}]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Nov 02 2009
STATUS
approved