OFFSET
1,2
COMMENTS
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 20.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
Let s(n) = Pi/2 - sum{2^h/((2h+1)*C(2h,h)), h = 1..n}. Approximations follow:
n ... s(n) ...... 1/3^n
1 ... 0.23746 ... 0.333333
2 ... 0.10413 ... 0.111111
3 ... 0.04698 ... 0.037037
4 ... 0.02159 ... 0.012345
5 ... 0.01004 ... 0.004115
6 ... 0.00471 ... 0.001371
7 ... 0.00223 ... 0.000472
a(5) = 7 because s(7) < 1/3^5 < s(6).
MATHEMATICA
z = 300; p[k_] := p[k] = Sum[2^h/((2 h + 1) Binomial[2 h, h]), {h, 0, k}]
d = N[Table[Pi/2 - p[k], {k, 1, z/5}], 12]
f[n_] := f[n] = Select[Range[z], Pi/2 - p[#] < 1/3^n &, 1]
u = Flatten[Table[f[n], {n, 1, z}]] (* A248607 *)
d = Differences[u]
v = Flatten[Position[d, 1]] (* A248608 *)
w = Flatten[Position[d, 2]] (* A248609 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 10 2014
STATUS
approved