A388613 Decimal expansion of (2*2^(3/4) * sqrt((2+sqrt(2)) / Pi) * Gamma(5/4)^2) / Pi.

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

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} A133692(k) / exp(k*Pi).

Example

0.91699125162111728822615110058655560858...

Mathematica

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

Prog

(PARI) (1/8) * 2^(1/4) * gamma(5/8)^2 * (2+2^(1/2))^(3/2) / sqrt(Pi) / gamma(7/8)^2

Crossrefs

Cf. A133692.

Sequence in context: A389050 A389046 A296473 * A388874 A213916 A297815

Adjacent sequences: A388610 A388611 A388612 * A388614 A388615 A388616

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved