A389071 Decimal expansion of (2^(2/3) * Gamma(3/4)^(7/3) * (((1+sqrt(3)) * Gamma(2/3)) / Gamma(11/12))^(1/3)) / (3^(7/12) * Pi^(1/6) * Gamma(7/12) * Gamma(11/12)).

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

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} A385520(k) / exp(k*Pi).

Equals 2^(5/12) * (1 + sqrt(3))^(1/6) / 3^(3/8). - Vaclav Kotesovec, Jan 09 2026

Example

1.0453382042005594559752927821917984628...

Mathematica

First[RealDigits[(2^(2/3)*Gamma[3/4]^(7/3)*(((1 + Sqrt[3])*Gamma[2/3])/Gamma[11/12])^(1/3))/(3^(7/12)*Pi^(1/6)*Gamma[7/12]*Gamma[11/12]), 10, 100]]
RealDigits[2^(5/12)*(1 + Sqrt[3])^(1/6)/3^(3/8), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1/6) * 3^(5/12) * gamma(2/3)^(1/3) * gamma(3/4)^(7/3) * (2^(1/2) * (1+3^(1/2)))^(4/3) * (3^(1/2)-1) / gamma(7/12) / Pi^(1/6) / gamma(11/12)^(4/3)

Crossrefs

Cf. A385520.

Sequence in context: A370634 A138753 A179410 * A272874 A008962 A175725

Adjacent sequences: A389068 A389069 A389070 * A389072 A389073 A389074

Keyword

nonn,cons

Author

Simon Plouffe, Sep 22 2025

Status

approved