A388576 Decimal expansion of ((-2+sqrt(5)) * sqrt((5/2+sqrt(5)) * Pi) * exp((2 * Pi) / 3)) / (2^(5/8) * 5^(3/4) * Gamma(3/4)^2).

9, 5, 4, 9, 1, 8, 6, 4, 6, 0, 7, 9, 7, 6, 2, 7, 9, 3, 1, 4, 7, 7, 7, 1, 9, 3, 0, 4, 1, 3, 4, 6, 0, 2, 7, 6, 4, 1, 4, 1, 7, 1, 2, 6, 5, 9, 4, 4, 5, 5, 5, 7, 3, 9, 2, 6, 0, 4, 0, 4, 9, 2, 6, 5, 7, 3, 5, 2, 8, 2, 5, 6, 8, 7, 3, 1, 7, 4, 2, 0, 3, 3, 8, 5, 9, 1, 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} A123759(k) / exp(k*Pi).

Example

0.95491864607976279314777193041346027639...

Mathematica

First[RealDigits[((-2 + Sqrt[5])*Sqrt[(5/2 + Sqrt[5])*Pi]*Exp[(2*Pi)/3])/(2^(5/8)*5^(3/4)*Gamma[3/4]^2), 10, 100]]

Prog

(PARI) (1/51200) * exp(2/3 * Pi) * sqrt(Pi) * 2^(11/40) * 5^(3/4) * gamma(4/5)^6 * (5-5^(1/2))^3 * (5^(1/2)-1)^3 * (5^(1/2)+1)^3 / gamma(9/10)^3 / gamma(7/10)^3 / gamma(3/4)^2

Crossrefs

Cf. A123759.

Sequence in context: A353772 A388879 A388609 * A259148 A388462 A089491

Adjacent sequences: A388573 A388574 A388575 * A388577 A388578 A388579

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved