A388805 Decimal expansion of (3^(3/4) * exp(-Pi/12) * ((-2 * (1+sqrt(3)) * Gamma(2/3) * Gamma(3/4)) / Gamma(-1/12))^(2/3)) / Pi^(1/3).

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

Offset

0,1

Links

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

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

Formula

Empirical: Equals Sum_{k>=0} A227398(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(1/3) / (2^(1/6) * exp(Pi/12)). - Vaclav Kotesovec, Jan 08 2026

Example

0.95857602310480450404074974658124051315...

Mathematica

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

Prog

(PARI) (1/2) * exp(-1/12 * Pi) * 3^(1/12) * gamma(2/3)^(2/3) * gamma(3/4)^(2/3) * (2^(1/2) * (1+3^(1/2)))^(2/3) / gamma(11/12)^(2/3) / Pi^(1/3)

Crossrefs

Cf. A227398.

Sequence in context: A388937 A393357 A388897 * A388614 A388648 A309645

Adjacent sequences: A388802 A388803 A388804 * A388806 A388807 A388808

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved