A388602 Decimal expansion of (1/3) * Pi^(1/3) * 3^(2/3) * Gamma(3/4)^(4/3) * (sqrt(2) * (1+3^(1/2)))^(1/3) / Gamma(11/12)^(1/3) / Gamma(7/12) / Gamma(2/3)^(2/3).

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

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} A132972(k) / exp(k*Pi).

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

Example

1.096817029153923530580228342846394177273091443155...

Mathematica

First[RealDigits[2^(5/6) * Gamma[3/4]^(4/3) * CubeRoot[-Pi*(Sqrt[3] + 1) /  Gamma[-1/12]] / (Gamma[7/12] * Gamma[2/3]^(2/3)), 10, 100]] (* Paolo Xausa, Jan 07 2026 *)
RealDigits[(1 + Sqrt[3])^(2/3) / 2^(5/6), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) (1/3) * Pi^(1/3) * 3^(2/3) * gamma(3/4)^(4/3) * (2^(1/2) * (1+3^(1/2)))^(1/3) / gamma(11/12)^(1/3) / gamma(7/12) / gamma(2/3)^(2/3)

Crossrefs

Cf. A132972.

Sequence in context: A157989 A243265 A248472 * A306553 A011194 A235916

Adjacent sequences: A388599 A388600 A388601 * A388603 A388604 A388605

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved