A388960 Decimal expansion of (2*2^(7/12) * Gamma(7/12) * Gamma(3/4)^(8/3) * Gamma(11/12)^(4/3)) / (3^(1/6) * Pi^(13/12) * ((1+sqrt(3)) * Gamma(2/3))^(1/3)).

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

Offset

1,2

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} A277283(k) / exp(k*Pi).

Equals 2^(13/3) * Pi^(15/4) / (3^(3/8) * (1 + sqrt(3))^(1/6) * Gamma(1/4)^5). - Vaclav Kotesovec, Jan 09 2026

Example

1.3188680966089846611920574920242722162...

Mathematica

First[RealDigits[(2*2^(7/12)*Gamma[7/12]*Gamma[3/4]^(8/3)*Gamma[11/12]^(4/3))/(3^(1/6)*Pi^(13/12)*((1 + Sqrt[3])*Gamma[2/3])^(1/3)), 10, 100]]
RealDigits[2^(13/3)*Pi^(15/4) / (3^(3/8)*(1 + Sqrt[3])^(1/6)*Gamma[1/4]^5), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (4/3) * 2^(1/4) * 3^(5/6) * gamma(3/4)^(8/3) * gamma(11/12)^(4/3) * gamma(7/12) / (2^(1/2) * (1+3^(1/2)))^(4/3) * (1+3^(1/2)) / Pi^(13/12) / gamma(2/3)^(1/3)

Crossrefs

Cf. A277283.

Sequence in context: A007023 A176103 A388099 * A388353 A308666 A076238

Adjacent sequences: A388957 A388958 A388959 * A388961 A388962 A388963

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved