A388708 Decimal expansion of (-32 * sqrt((4+2 * sqrt(5)+sqrt(3 * (9+4 * sqrt(5)))) / 5) * Gamma(7/12) * Gamma(2/3)) / Gamma(-1/4)^3.

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

Offset

1,6

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Simon Plouffe, Numbers in the base e^Pi, 2025.

Formula

Empirical: Equals Sum_{k>=0} A192323(k) / exp(k*Pi).

Equals (1 + sqrt(5))^(3/2) * sqrt(1 + sqrt(3)) * Gamma(1/4)^2 / (2^(11/4) * 3^(3/8) * 5^(1/2) * Pi^(3/2)). - Vaclav Kotesovec, Jan 07 2026

Example

1.0001617004872419988720870205864935648...

Mathematica

First[RealDigits[Gamma[2/3]*Gamma[7/12]*5^(3/4)*(5 - Sqrt[5])^(3/2)*(1 + Sqrt[3])*(1 + Sqrt[5])^3/(1600*Gamma[3/4]^3), 10, 100]] (* Paolo Xausa, Sep 20 2025 *)
RealDigits[(1 + Sqrt[5])^(3/2) * Sqrt[1 + Sqrt[3]] * Gamma[1/4]^2 / (2^(11/4)*3^(3/8)*5^(1/2)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) (1/1600) * 5^(3/4) * gamma(2/3) * gamma(7/12) * (5-5^(1/2))^(3/2) * (1+3^(1/2)) * (5^(1/2)+1)^3 / gamma(3/4)^3

Crossrefs

Cf. A192323.

Sequence in context: A366868 A127778 A076714 * A299620 A113811 A126168

Adjacent sequences: A388705 A388706 A388707 * A388709 A388710 A388711

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved