A388590 Decimal expansion of ((-1+sqrt(3)) * Pi * exp(Pi / 3) * Gamma(11/12)) / (sqrt(6) * Gamma(2/3) * Gamma(3/4)^3).

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A129576(k) / exp(k*Pi).

Equals exp(Pi/3) * Gamma(1/4)^2 / (2^(5/4) * 3^(3/8) * Pi^(3/2) * sqrt(1 + sqrt(3))). - Vaclav Kotesovec, Jan 08 2026

Example

1.13338408008481238894056938793527580059726731866876807756245842276382347252....

Mathematica

First[RealDigits[((-1 + Sqrt[3])*Pi*Exp[Pi/3]*Gamma[11/12])/(Sqrt[6]*Gamma[2/3]*Gamma[3/4]^3), 10, 100]]
RealDigits[E^(Pi/3)*Gamma[1/4]^2 / (2^(5/4)*3^(3/8)*Pi^(3/2)*Sqrt[1 + Sqrt[3]]), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/6) * exp(Pi / 3) * Pi * 3^(1/2) * gamma(11/12) * sqrt(2) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)^3
(PARI) exp(Pi/3)*gamma(1/4)^2/(2^(5/4)*3^(3/8)*Pi^(3/2)*sqrt(1+sqrt(3))) \\ Charles R Greathouse IV, Jul 12 2026

Crossrefs

Cf. A129576.

Sequence in context: A111521 A177937 A029628 * A396370 A346159 A241739

Adjacent sequences: A388587 A388588 A388589 * A388591 A388592 A388593

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved