A389011 Decimal expansion of (9/2048) * exp(5*Pi/6) * 3^(1/2) * Gamma(2/3)^5 * Gamma(11/12)^7 * Gamma(7/12)^12 * (2+3^(1/2)) / Pi / Gamma(3/4)^25.

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

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} A280822(k) / exp(k*Pi).

Equals exp(5*Pi/6) * Gamma(1/4)^6 / (2^(21/4) * 3^(9/8) * sqrt(1 + sqrt(3)) * Pi^(9/2)). - Vaclav Kotesovec, Jan 09 2026

Example

0.83306529693958893252783356734652721578...

Mathematica

First[RealDigits[(9*(3 + 2*Sqrt[3])*Exp[(5*Pi)/6]*Gamma[7/12]^12*Gamma[2/3]^5*Gamma[11/12]^7)/(2048*Pi*Gamma[3/4]^25), 10, 100]]
RealDigits[E^(5*Pi/6)*Gamma[1/4]^6 / (2^(21/4)*3^(9/8)*Sqrt[1 + Sqrt[3]]*Pi^(9/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (9/2048) * exp(5/6 * Pi) * 3^(1/2) * gamma(2/3)^5 * gamma(11/12)^7 * gamma(7/12)^12 * (2+3^(1/2)) / Pi / gamma(3/4)^25

Crossrefs

Cf. A280822.

Sequence in context: A387468 A197729 A388770 * A369049 A010148 A246822

Adjacent sequences: A389008 A389009 A389010 * A389012 A389013 A389014

Keyword

nonn,cons

Author

Simon Plouffe, Sep 22 2025

Status

approved