A365255 Decimal expansion of Product_{n>=2} cos(Pi/(2*n)).

4, 2, 9, 7, 8, 0, 2, 1, 6, 4, 3, 7, 9, 9, 1, 7, 0, 6, 5, 8, 4, 7, 8, 9, 5, 1, 4, 7, 0, 6, 3, 3, 0, 4, 8, 8, 4, 9, 2, 5, 3, 7, 6, 3, 9, 7, 4, 5, 4, 8, 6, 5, 7, 1, 0, 8, 2, 7, 6, 5, 7, 3, 7, 4, 3, 6, 8, 8, 3, 3, 6, 8, 8, 4, 3, 7, 2, 9, 1, 5, 9, 5, 3, 1, 0

Offset

0,1

Links

Table of n, a(n) for n=0..84.

Formula

this * A365256 = A085365.

Equals exp(-Sum_{k>=1} (zeta(2*k) * (zeta(2*k)-1) * (1 - 1/4^k) / k)). - Amiram Eldar, Jun 26 2026

Example

0.4297802164379917065847895147063304...

Mathematica

With[{m = 1000}, RealDigits[Exp[-NSum[(1 - 1/4^k)*Zeta[2*k] (Zeta[2*k] - 1)/k, {k, 1, Infinity}, WorkingPrecision -> m, PrecisionGoal -> m, AccuracyGoal -> m, NSumTerms -> m]], 10, 120][[1]]] (* Amiram Eldar, Jun 26 2026 *)

Prog

(PARI) exp(sumpos(n=2, log(cos(Pi/(2*n))))) \\ Michel Marcus, Aug 29 2023

Crossrefs

Cf. A085365, A365256.

Sequence in context: A237126 A246380 A200639 * A243968 A104583 A278103

Adjacent sequences: A365252 A365253 A365254 * A365256 A365257 A365258

Keyword

cons,nonn

Author

R. J. Mathar, Aug 29 2023

Status

approved