A388596 Decimal expansion of (1/6) * 3^(3/4) * Gamma(2/3) * Gamma(3/4) * (1+3^(1/2)) / Gamma(11/12) / sqrt(Pi).

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

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

Index entries for algebraic numbers, degree 8.

Formula

Empirical: Equals Sum_{k>=0} A132002(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) / (2^(1/4) * 3^(3/8)). - Vaclav Kotesovec, Jan 08 2026

Example

0.92059034625205082371506807162697840363...

Mathematica

First[RealDigits[(-2*3^(3/4)*(1 + Sqrt[3])*Gamma[2/3]*Gamma[3/4])/(Sqrt[Pi]*Gamma[-1/12]), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[3]]/(2^(1/4)*3^(3/8)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/6) * 3^(3/4) * gamma(2/3) * gamma(3/4) * (1+3^(1/2)) / gamma(11/12) / sqrt(Pi)
(PARI) sqrt(1+sqrt(3))/(2^(1/4)*3^(3/8)) \\ Charles R Greathouse IV, Jul 12 2026
(PARI) polrootsreal(27*x^8 - 18*x^4 - 1)[2] \\ Charles R Greathouse IV, Jul 12 2026

Crossrefs

Cf. A132002.

Sequence in context: A388754 A019876 A155696 * A098875 A147711 A388697

Adjacent sequences: A388593 A388594 A388595 * A388597 A388598 A388599

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved