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(4/3) - sum{1/(h*4^h), h = 1..n}. Approximations follow:
n ... s(n) ........ 1/8^n
1 ... 0.037682 ... 0.125
2 ... 0.006432 ... 0.015625
3 ... 0.001223 ... 0.001953
4 ... 0.000247 ... 0.000244
5 ... 0.000051 ... 0.000030
a(4) = 5 because s(5) < 1/8^4 < s(4).
MATHEMATICA
z = 2500; p[k_] := p[k] = Sum[1/(h*4^h), {h, 1, k}];
N[Table[p[k], {k, 1, z/5}], 12];
N[Table[Log[4/3] - p[n], {n, 1, z/5}]];
f[n_] := f[n] = Select[Range[z], Log[4/3] - p[#] < 1/8^n &, 1];
u = Flatten[Table[f[n], {n, 1, z}]] ; (* A248565 *)
Flatten[Position[Differences[u], 1]]; (* A248566 *)
Flatten[Position[Differences[u], 2]]; (* A248567 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 09 2014
STATUS
approved