A388949 Decimal expansion of ((-3+sqrt(3)) * sqrt(Pi) * exp(Pi / 3) * Gamma(11/12)) / (2^(3/8) * Gamma(-1/3) * Gamma(3/4)).

1, 0, 4, 7, 1, 2, 4, 9, 6, 0, 7, 4, 6, 4, 6, 4, 0, 0, 0, 8, 9, 0, 3, 9, 4, 6, 0, 0, 8, 4, 4, 3, 6, 3, 0, 3, 0, 8, 6, 6, 0, 2, 9, 5, 8, 8, 0, 6, 9, 7, 1, 5, 1, 1, 2, 4, 5, 6, 5, 8, 5, 1, 4, 3, 8, 7, 5, 4, 6, 9, 9, 4, 7, 8, 2, 1, 3, 3, 2, 2, 8, 2, 2, 9, 7, 4, 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} A271593(k) / exp(k*Pi).

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

Example

1.0471249607464640008903946008443630308...

Mathematica

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

Prog

(PARI) (1/6) * exp(Pi / 3) * sqrt(Pi) * 2^(5/8) * 3^(1/2) * gamma(11/12) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)

Crossrefs

Cf. A271593.

Sequence in context: A254338 A197723 A186191 * A388336 A256507 A123734

Adjacent sequences: A388946 A388947 A388948 * A388950 A388951 A388952

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved