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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 19:58 EDT 2019. Contains 328315 sequences. (Running on oeis4.)