A388798 Decimal expansion of (Pi^(2/3) * (((-1+sqrt(3)) * Gamma(11/12)) / Gamma(5/3))^(1/3)) / (2^(1/6) * Gamma(3/4)^(7/3)).

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

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} A226535(k) / exp(k*Pi).

Equals 3^(3/8) * Gamma(1/4)^2 / (2^(17/12) * (1 + sqrt(3))^(1/6) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.1291470973442343435923033949907007072...

Mathematica

First[RealDigits[(Pi^(2/3)*(((-1 + Sqrt[3])*Gamma[11/12])/Gamma[5/3])^(1/3))/(2^(1/6)*Gamma[3/4]^(7/3)), 10, 100]]
RealDigits[3^(3/8)*Gamma[1/4]^2 / (2^(17/12)*(1 + Sqrt[3])^(1/6)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A226535.

Sequence in context: A272868 A378352 A074950 * A346170 A113211 A244807

Adjacent sequences: A388795 A388796 A388797 * A388799 A388800 A388801

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved