A388775 Decimal expansion of (1/3) * exp(5*Pi/24) * 2^(3/8) * 3^(7/12) * Pi^(1/6) * Gamma(11/12)^(1/3) / (sqrt(2) * (1+3^(1/2)))^(1/3) / Gamma(2/3)^(1/3) / Gamma(3/4)^(1/3).

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

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Formula

Empirical: Equals Sum_{k>=0} A219601(k) / exp(k*Pi).

Equals exp(5*Pi/24) / (2^(1/24) * 3^(3/8) * (1 + sqrt(3))^(1/6)). - Vaclav Kotesovec, Jan 07 2026

Example

1.0472094632261824240604159887932382773...

Mathematica

First[RealDigits[2^(5/24) * Exp[5*Pi/24] * Pi^(1/6) * CubeRoot[Gamma[11/12] / ((Sqrt[3] + 1) * Gamma[2/3] * Gamma[3/4])] / 3^(5/12), 10, 100]] (* Paolo Xausa, Jan 07 2026 *)
RealDigits[E^(5*Pi/24) / (2^(1/24) * 3^(3/8) * (1 + Sqrt[3])^(1/6)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) (1/3) * exp(5/24 * Pi) * 2^(3/8) * 3^(7/12) * Pi^(1/6) * gamma(11/12)^(1/3) / (2^(1/2) * (1+3^(1/2)))^(1/3) / gamma(2/3)^(1/3) / gamma(3/4)^(1/3)

Crossrefs

Cf. A219601.

Sequence in context: A246710 A388094 A388461 * A388691 A388909 A388933

Adjacent sequences: A388772 A388773 A388774 * A388776 A388777 A388778

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved