A389010 Decimal expansion of ((1+sqrt(3))^(5/3) * Pi^(5/4) * ((-1+sqrt(3)) / (Gamma(7/12) * Gamma(11/12)))^(3/2)) / (4*2^(7/12) * Gamma(3/4)^2).

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

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} A280666(k) / exp(k*Pi).

Equals 3^(3/8) * (1 + sqrt(3))^(1/6) * Gamma(1/4)^5 / (2^(13/3) * Pi^(15/4)). - Vaclav Kotesovec, Jan 09 2026

Example

0.75822593826566567721284364705122610165...

Mathematica

First[RealDigits[((1 + Sqrt[3])^(5/3)*Pi^(5/4)*((-1 + Sqrt[3])/(Gamma[7/12]*Gamma[11/12]))^(3/2))/(4*2^(7/12)*Gamma[3/4]^2), 10, 100]]
RealDigits[3^(3/8)*(1 + Sqrt[3])^(1/6)*Gamma[1/4]^5 / (2^(13/3)*Pi^(15/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1/32) * Pi^(5/4) * 2^(5/6) * (2^(1/2) * (3^(1/2)-1))^(3/2) * (2^(1/2) * (1+3^(1/2)))^(5/3) / gamma(3/4)^2 / gamma(11/12)^(3/2) / gamma(7/12)^(3/2)

Crossrefs

Cf. A280666.

Sequence in context: A111769 A111513 A388089 * A280722 A262899 A198922

Adjacent sequences: A389007 A389008 A389009 * A389011 A389012 A389013

Keyword

nonn,cons

Author

Simon Plouffe, Sep 22 2025

Status

approved