A388747 Decimal expansion of (exp(Pi / 6) * (-(((1+sqrt(3)) * Pi * Gamma(2/3)) / Gamma(-1/12)))^(1/3)) / (2^(1/6) * Gamma(3/4)^(5/3)).

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

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} A208978(k) / exp(k*Pi).

Equals exp(Pi/6) * (1 + sqrt(3))^(1/6) * Gamma(1/4)^2 / (2^(19/12) * 3^(3/8) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0414303539132480988035534226451395764...

Mathematica

First[RealDigits[(Exp[Pi/6]*(-(((1 + Sqrt[3])*Pi*Gamma[2/3])/Gamma[-1/12]))^(1/3))/(2^(1/6)*Gamma[3/4]^(5/3)), 10, 100]]
RealDigits[E^(Pi/6) * (1 + Sqrt[3])^(1/6) * Gamma[1/4]^2 / (2^(19/12) * 3^(3/8) * Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A208978.

Sequence in context: A161772 A093063 A324937 * A049007 A377120 A016686

Adjacent sequences: A388744 A388745 A388746 * A388748 A388749 A388750

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved