A388945 Decimal expansion of (3^(3/4) * (1+sqrt(3)) * exp(-Pi/3) * Gamma(3/4)^3 * Gamma(5/3)) / (Pi * Gamma(11/12)).

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

Offset

1,3

Links

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

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

Formula

Empirical: Equals Sum_{k>=0} A263993(k) / exp(k*Pi).

Equals 2^(11/4) * Pi^(3/2) * sqrt(1 + sqrt(3)) / (3^(3/8) * exp(Pi/3) * Gamma(1/4)^2). - Vaclav Kotesovec, Jan 09 2026

Example

1.0947802255259739831207132829411463447...

Mathematica

First[RealDigits[(3^(3/4)*(1 + Sqrt[3])*Exp[-1/3*Pi]*Gamma[3/4]^3*Gamma[5/3])/(Pi*Gamma[11/12]), 10, 100]]
RealDigits[2^(11/4) * Pi^(3/2) * Sqrt[1 + Sqrt[3]] / (3^(3/8) * E^(Pi/3) * Gamma[1/4]^2), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

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

Crossrefs

Cf. A263993.

Sequence in context: A065466 A388963 A122790 * A388164 A288241 A199665

Adjacent sequences: A388942 A388943 A388944 * A388946 A388947 A388948

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved