A388477 Decimal expansion of ((3 / Pi)^(1/12) * (((1+sqrt(3)) * Gamma(2/3)) / Gamma(11/12))^(2/3)) / (2*2^(1/6) * Gamma(3/4)^(1/3)).

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

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} A089807(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(1/3) * Gamma(1/4) / (2^(7/6) * Pi^(3/4)). - Vaclav Kotesovec, Jan 08 2026

Example

0.95678259439492263826514387381145502998...

Mathematica

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

Prog

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

Crossrefs

Cf. A089807.

Sequence in context: A292824 A388932 A388671 * A388624 A388891 A388682

Adjacent sequences: A388474 A388475 A388476 * A388478 A388479 A388480

Keyword

nonn,cons

Author

Simon Plouffe, Sep 17 2025

Status

approved