A388682 Decimal expansion of (2^(3/8) * (2+sqrt(3))^(1/3) * Pi^(1/4) * exp(Pi / 12)) / sqrt(3 * (1+sqrt(3)) * Gamma(7/12) * Gamma(11/12)).

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

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} A164562(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(1/6) * exp(Pi/12) * Gamma(1/4) / (2^(17/24) * 3^(3/8) * Pi^(3/4)). - Vaclav Kotesovec, Jan 08 2026

Example

0.95678592481567745894989096320813770262...

Mathematica

First[RealDigits[(2^(3/8)*(2 + Sqrt[3])^(1/3)*Pi^(1/4)*Exp[Pi/12])/Sqrt[3*(1 + Sqrt[3])*Gamma[7/12]*Gamma[11/12]], 10, 100]]
RealDigits[(1 + Sqrt[3])^(1/6) * E^(Pi/12) * Gamma[1/4] / (2^(17/24)*3^(3/8)*Pi^(3/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/12) * exp(Pi / 12) * Pi^(1/4) * 2^(23/24) * 3^(1/2) * (2^(1/2) * (3^(1/2)-1))^(1/2) * (2^(1/2) * (1+3^(1/2)))^(2/3) / gamma(11/12)^(1/2) / gamma(7/12)^(1/2)

Crossrefs

Cf. A164562.

Sequence in context: A388477 A388624 A388891 * A388610 A334826 A021515

Adjacent sequences: A388679 A388680 A388681 * A388683 A388684 A388685

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved