A388583 Decimal expansion of (16 * (2+sqrt(2)) * (-3+sqrt(3)) * exp((5 * Pi) / 6) * Gamma(11/12) * Gamma(5/4)^3 * sin(Pi / 8)^3) / (Pi^2 * Gamma(-1/3)).

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

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

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A128582(k) / exp(k*Pi).

Equals exp(5*Pi/6) * Gamma(1/4)^2 / (8*Pi * 3^(3/8) * sqrt((1 + sqrt(2)) * (1 + sqrt(3))*Pi)). - Vaclav Kotesovec, Jan 08 2026

Example

1.04321770702227072866578717731094116578714993185463770961802391989891673971....

Mathematica

First[RealDigits[(16*(2 + Sqrt[2])*(-3 + Sqrt[3])*Exp[(5*Pi)/6]*Gamma[11/12]*Gamma[5/4]^3*Sin[Pi/8]^3)/(Pi^2*Gamma[-1/3]), 10, 100]]
RealDigits[E^(5*Pi/6)*Gamma[1/4]^2/(8*3^(3/8)*Pi*Sqrt[(1 + Sqrt[2])*(1 + Sqrt[3])*Pi]), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/96) * exp(5/6 * Pi) * 2^(3/4) * 3^(1/2) * gamma(5/8)^3 * gamma(11/12) * (2+2^(1/2)) * (3^(1/2)-1) / gamma(2/3) / gamma(7/8)^3 / sqrt(Pi)
(PARI) exp(5*Pi/6)*gamma(1/4)^2/(8*3^(3/8)*sqrt((1+sqrt(2))*(1+sqrt(3))*Pi)*Pi) \\ Charles R Greathouse IV, Jul 14 2026

Crossrefs

Cf. A128582.

Sequence in context: A194764 A194738 A194750 * A370350 A194743 A113778

Adjacent sequences: A388580 A388581 A388582 * A388584 A388585 A388586

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved