A388649 Decimal expansion of (2^(1/8) * (-3+sqrt(3)) * sqrt(Pi) * exp((5 * Pi) / 24) * Gamma(11/12)) / (Gamma(-1/3) * Gamma(3/4)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Formula

Empirical: Equals Sum_{k>=0} A143067(k) / exp(k*Pi).

Equals (2/3)^(3/8) * exp(5*Pi/24) / sqrt(1 + sqrt(3)). - Vaclav Kotesovec, Jan 08 2026

Example

0.99992278756715478607762363717504850859...

Mathematica

First[RealDigits[(2^(1/8)*(-3 + Sqrt[3])*Sqrt[Pi]*Exp[(5*Pi)/24]*Gamma[11/12])/(Gamma[-1/3]*Gamma[3/4]), 10, 100]]
RealDigits[(2/3)^(3/8) * E^(5*Pi/24) / Sqrt[1 + Sqrt[3]], 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/3) * exp(5/24 * Pi) * sqrt(Pi) * 2^(1/8) * 3^(1/2) * gamma(11/12) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)

Crossrefs

Cf. A143067.

Sequence in context: A348294 A018938 A292888 * A111659 A346450 A102819

Adjacent sequences: A388646 A388647 A388648 * A388650 A388651 A388652

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved