A389054 Decimal expansion of (8 * (1+sqrt(2)) * sqrt(5-sqrt(5)) * (3+sqrt(5)) * Gamma(5/4)^4) / (5^(3/4) * Pi^3).

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

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} A320151(k) / exp(k*Pi).

Example

1.0945657154193823122175866877715034293...

Mathematica

First[RealDigits[(8*(1 + Sqrt[2])*Sqrt[5 - Sqrt[5]]*(3 + Sqrt[5])*Gamma[5/4]^4)/(5^(3/4)*Pi^3), 10, 100]]

Prog

(PARI) (1/25600) * 5^(3/4) * gamma(5/8)^4 * (3+2 * sqrt(2)) * sqrt(2) * (5-5^(1/2))^(3/2) * (4+2 * sqrt(2)) * (5^(1/2)+1)^3 / Pi / gamma(7/8)^4

Crossrefs

Cf. A320151.

Sequence in context: A021518 A030070 A388837 * A114739 A388886 A240964

Adjacent sequences: A389051 A389052 A389053 * A389055 A389056 A389057

Keyword

nonn,cons

Author

Simon Plouffe, Sep 22 2025

Status

approved