A388839 Decimal expansion of ((-3+sqrt(3)) * Pi * exp(Pi / 3) * Gamma(11/12)) / (2^(3/4) * Gamma(-1/3) * Gamma(3/4)^3).

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

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} A246752(k) / exp(k*Pi).

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

Example

0.95305861004894765776518114212209644443...

Mathematica

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

Prog

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

Crossrefs

Cf. A246752.

Sequence in context: A021917 A128757 A195599 * A021516 A388386 A388678

Adjacent sequences: A388836 A388837 A388838 * A388840 A388841 A388842

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved