A389029 Decimal expansion of (Pi^(5/3) * exp(Pi) * Gamma(7/12)^(11/2) * Gamma(11/12)^(47/6)) / (4*2^(1/6) * 3^(1/24) * ((1+sqrt(3)) * Gamma(2/3))^(7/3) * Gamma(3/4)^(46/3)).

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

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} A293422(k) / exp(k*Pi).

Equals exp(Pi) * Gamma(1/4)^2 / (2^(13/6) * 3^(9/8) * (1 + sqrt(3))^(7/6) * Pi^(3/2)). - Vaclav Kotesovec, Jan 09 2026

Example

1.0944192563140623458857728610518713872...

Mathematica

First[RealDigits[(Pi^(5/3)*Exp[Pi]*Gamma[7/12]^(11/2)*Gamma[11/12]^(47/6))/(4*2^(1/6)*3^(1/24)*((1 + Sqrt[3])*Gamma[2/3])^(7/3)*Gamma[3/4]^(46/3)), 10, 100]]
RealDigits[E^Pi * Gamma[1/4]^2 / (2^(13/6) * 3^(9/8) * (1 + Sqrt[3])^(7/6) * Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1024/3) * exp(Pi) * Pi^(5/3) * 3^(23/24) * gamma(7/12)^(11/2) * gamma(11/12)^(47/6) / gamma(2/3)^(7/3) / gamma(3/4)^(46/3) / (2^(1/2) * (1+3^(1/2)))^(47/6) / (2^(1/2) * (3^(1/2)-1))^(11/2)

Crossrefs

Cf. A293422.

Sequence in context: A117018 A193712 A382573 * A388955 A249600 A375274

Adjacent sequences: A389026 A389027 A389028 * A389030 A389031 A389032

Keyword

nonn,cons

Author

Simon Plouffe, Sep 22 2025

Status

approved