OFFSET
1,2
COMMENTS
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 14.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
FORMULA
a(n) ~ ceiling(n*sqrt(e/6)). - Thomas Scheuerle, Dec 08 2025
EXAMPLE
Approximations are shown here:
n ... ((2*n+1)/(2*n-1))^n - e ... 1/(2*n^2)
1 ... 0.281718 .................. 0.5
2 ... 0.0594959 ................. 0.125
3 ... 0.0257182 ................. 0.05555
4 ... 0.0143296 ................. 0.03125
a(4) = 3 because p(4) - e < 1/32 < p(3) - e.
MATHEMATICA
z = 1200; p[k_] := p[k] = ((2 k + 1)/(2 k - 1))^k;
N[Table[p[n] - E, {n, 1, z/8}]]
f[n_] := f[n] = Select[Range[z], p[#] - E < 1/(2 n^2) &, 1]
u = Flatten[Table[f[n], {n, 1, z/10}]] (* A248103 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 02 2014
EXTENSIONS
Name corrected by Thomas Scheuerle, Dec 09 2025
STATUS
approved