A067744 Number of terms yielding particularly small errors in a numerical integration of exp((cos(x)-1)/(cos(x)+1)) having non-monotonic sub-geometric convergence.

2, 4, 7, 11, 16, 20, 26, 31, 37, 43, 50, 56, 64, 71, 79, 86, 95, 103, 112, 120, 129, 139, 148, 158, 168, 178, 188, 199, 209, 220, 231, 243, 254, 266, 277, 289, 301, 314, 326, 338, 351, 364, 377, 390, 404, 417, 431, 444, 458, 472, 487, 501, 515, 530, 545, 560

Offset

2,1

Links

Table of n, a(n) for n=2..57.

J. A. C. Weideman, Numerical Integration of Periodic Functions: A Few Examples, Amer. Math. Monthly, 109 (2002), 30-32.

Formula

a(n) = round(((2*Pi/(3^(3/2)))*((6*n-5)/6))^(3/2)).

Example

a(2)=2 since 7*sqrt(7)*Pi^(3/2) / (27 3^(3/4)) = 1.6755877...

Mathematica

Table[Round[((2 Pi/(3^(3/2))) ((6 n - 5)/6))^(3/2)], {n, 2, 57}] (* Michael De Vlieger, Sep 29 2017 *)

Prog

(PARI) a(n) = round(((2*Pi/(3^(3/2)))*((6*n-5)/6))^(3/2)); \\ Michel Marcus, Sep 29 2017

Crossrefs

Sequence in context: A299251 A238485 A316264 * A307601 A194215 A025718

Adjacent sequences: A067741 A067742 A067743 * A067745 A067746 A067747

Keyword

easy,nonn

Author

Marc LeBrun, Jan 29 2002

Status

approved