A388943 Decimal expansion of (Pi^(4/3) * (((-1+sqrt(3)) * Gamma(11/12)) / Gamma(5/3))^(2/3)) / (2^(1/3) * Gamma(3/4)^(14/3)).

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

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} A263773(k) / exp(k*Pi).

Equals 3^(3/4) * Gamma(1/4)^4 / (2^(17/6) * (1 + sqrt(3))^(1/3) * Pi^3). - Vaclav Kotesovec, Jan 09 2026

Example

1.2749731674409098286283971433024120804...

Mathematica

First[RealDigits[(Pi^(4/3)*(((-1 + Sqrt[3])*Gamma[11/12])/Gamma[5/3])^(2/3))/(2^(1/3)*Gamma[3/4]^(14/3)), 10, 100]]
RealDigits[3^(3/4) * Gamma[1/4]^4 / (2^(17/6) * (1 + Sqrt[3])^(1/3) * Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) Pi^(4/3) * 3^(2/3) * gamma(11/12)^(2/3) / gamma(2/3)^(2/3) / gamma(3/4)^(14/3) / (2^(1/2) * (1+3^(1/2)))^(2/3)

Crossrefs

Cf. A263773.

Sequence in context: A388228 A222056 A247448 * A329064 A102514 A115857

Adjacent sequences: A388940 A388941 A388942 * A388944 A388945 A388946

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved