A388885 Decimal expansion of (1/4) * Pi^(1/12) * 3^(2/3) * Gamma(2/3)^(4/3) * Gamma(11/12)^(2/3) * Gamma(7/12)^2 * (2+3^(1/2)) / (sqrt(2) * (1+3^(1/2)))^(2/3) / Gamma(3/4)^(17/3).

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

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} A257653(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(2/3) * Gamma(1/4)^3 / (2^(17/6) * Pi^(9/4)). - Vaclav Kotesovec, Jan 08 2026

Example

0.99455820567394033256078848251053061964...

Mathematica

First[RealDigits[((2 + Sqrt[3])*Pi^(1/12)*Gamma[7/12]^2*Gamma[2/3]^(4/3)*(3*(-1 + Sqrt[3])*Gamma[11/12])^(2/3))/(8*Gamma[3/4]^(17/3)), 10, 100]]
RealDigits[(1 + Sqrt[3])^(2/3) * Gamma[1/4]^3 / (2^(17/6) * Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/4) * Pi^(1/12) * 3^(2/3) * gamma(2/3)^(4/3) * gamma(11/12)^(2/3) * gamma(7/12)^2 * (2+3^(1/2)) / (2^(1/2) * (1+3^(1/2)))^(2/3) / gamma(3/4)^(17/3)

Crossrefs

Cf. A257653.

Sequence in context: A019893 A346585 A117023 * A375070 A013668 A143302

Adjacent sequences: A388882 A388883 A388884 * A388886 A388887 A388888

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved