A388690 Decimal expansion of (sqrt(-1+sqrt(3)) * Pi^(3/4) * exp((19 * Pi) / 24) * (Gamma(7/12) * Gamma(11/12))^(9/2)) / (16*2^(1/8) * Gamma(3/4)^12).

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

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} A181648(k) / exp(k*Pi).

Equals sqrt(sqrt(3) - 1) * exp(19*Pi/24) * Gamma(1/4)^3 / (2^(27/8) * 3^(9/8) * Pi^(9/4)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0452501939334113989363653055347499836...

Mathematica

First[RealDigits[(Sqrt[-1 + Sqrt[3]]*Pi^(3/4)*Exp[(19*Pi)/24]*(Gamma[7/12]*Gamma[11/12])^(9/2))/(16*2^(1/8)*Gamma[3/4]^12), 10, 100]]
RealDigits[Sqrt[Sqrt[3] - 1] * E^(19*Pi/24) * Gamma[1/4]^3 / (2^(27/8)*3^(9/8)*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/16) * exp(19/24 * Pi) * Pi^(3/4) * 2^(1/8) * gamma(11/12)^(9/2) * gamma(7/12)^(9/2) * (3^(1/2)-1) / (2^(1/2) * (3^(1/2)-1))^(1/2) / gamma(3/4)^12

Crossrefs

Cf. A181648.

Sequence in context: A388452 A105662 A021225 * A292820 A388486 A388430

Adjacent sequences: A388687 A388688 A388689 * A388691 A388692 A388693

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved