OFFSET
1,2
COMMENTS
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 15.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
Let s(n) = log(2) - sum{1/(h*2^h), h = 1..n}. Approximations follow:
n ... s(n) ........ 1/3^n
1 ... 0.193147 .... 0.33333
2 ... 0.0681472 ... 0.11111
3 ... 0.0264805 ... 0.037037
4 ... 0.0108555 ... 0.0123457
5 ... 0.0046066 ... 0.004115
6 ... 0.0020013 ... 0.00137174
a(5) = 6 because s(6) < 1/3^5 < s(5).
MATHEMATICA
z = 200; p[k_] := p[k] = Sum[1/(h*2^h), {h, 1, k}]
N[Table[Log[2] - p[n], {n, 1, z/5}]]
f[n_] := f[n] = Select[Range[z], Log[2] - p[#] < 1/3^n &, 1]
u = Flatten[Table[f[n], {n, 1, z}]] (* A248559 *)
Flatten[Position[Differences[u], 1]] (* A248560 *)
Flatten[Position[Differences[u], 2]] (* A248561 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 09 2014
STATUS
approved