A388632 Decimal expansion of ((-1+sqrt(5)) * Pi * exp(Pi) * ((Pi * Gamma(9/10)) / Gamma(7/10))^(1/3)) / (10*2^(8/15) * 5^(7/12) * Gamma(3/5)^(2/3) * Gamma(3/4)^4).

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

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} A138483(k) / exp(k*Pi).

Equals exp(Pi) * Gamma(1/4)^4 / (2^(5/2) * 5^(3/2) * sqrt(1 + sqrt(5)) * Pi^3). - Vaclav Kotesovec, Jan 07 2026

Example

1.1334757218321992097617409943442575896...

Mathematica

First[RealDigits[((-1 + Sqrt[5])*Pi*Exp[Pi]*((Pi*Gamma[9/10])/Gamma[7/10])^(1/3))/(10*2^(8/15)*5^(7/12)*Gamma[3/5]^(2/3)*Gamma[3/4]^4), 10, 100]]
RealDigits[E^Pi * Gamma[1/4]^4 / (2^(5/2) * 5^(3/2) * Sqrt[1 + Sqrt[5]] * Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) 1/200 * exp(Pi) * Pi^(4/3) * 2^(4/5) * (5^(1/2)+1)^(1/3) * gamma(9/10)^(1/3) * (5^(1/2)-1)^(4/3) * 5^(5/12) / gamma(3/4)^4 / gamma(3/5)^(2/3) / gamma(7/10)^(1/3)

Crossrefs

Cf. A138483.

Sequence in context: A319526 A388869 A388600 * A258835 A007448 A155689

Adjacent sequences: A388629 A388630 A388631 * A388633 A388634 A388635

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved