A346745 Decimal expansion of Product_{k>=2} (1 - 1/k^12).

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Michael I. Shamos, Shamos's catalog of the real numbers (2011).

Formula

Equals sinh(Pi) * cosh(Pi*sqrt(3)/2)^2 * (cosh(Pi) - cos(Pi*sqrt(3))) / (24*Pi^5).

Equals exp(Sum_{j>=1} (1 - zeta(12*j))/j). - Vaclav Kotesovec, Aug 01 2021

Example

0.999753913921893256003448570641909727180...

Maple

evalf(sinh(Pi) * cosh(Pi*sqrt(3)/2)^2 * (cosh(Pi) - cos(Pi*sqrt(3))) / (24*Pi^5), 120); # Vaclav Kotesovec, Aug 01 2021

Mathematica

RealDigits[Sinh[Pi]*Cosh[Pi*Sqrt[3]/2]^2*(Cosh[Pi] - Cos[Pi*Sqrt[3]])/(24*Pi^5), 10, 120][[1]] (* Amiram Eldar, Jun 12 2023 *)

Prog

(PARI) exp(suminf(j=1, (1 - zeta(12*j))/j)) \\ Vaclav Kotesovec, Aug 01 2021

Crossrefs

Cf. A109219, A175615, A175616, A175617, A175618, A175619, A339745.

Sequence in context: A111590 A346584 A346571 * A307054 A346437 A346260

Adjacent sequences: A346742 A346743 A346744 * A346746 A346747 A346748

Keyword

nonn,cons

Author

Sean A. Irvine, Jul 31 2021

Status

approved