A388646 Decimal expansion of Gamma(3/4) * sqrt(2 * Pi) * (3^(1/2)-1) / Gamma(7/12) / Gamma(2/3).

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

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

Index entries for algebraic numbers, degree 8.

Formula

Empirical: Equals Sum_{k>=0} A139137(k) / exp(k*Pi).

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

Example

1.08625948997971286653304057122967007278150532832850899744806741057643487131....

Mathematica

First[RealDigits[((-1 + Sqrt[3])*Sqrt[2*Pi]*Gamma[3/4])/(Gamma[7/12]*Gamma[2/3]), 10, 100]]
RealDigits[2^(1/4)*3^(3/8)/Sqrt[1 + Sqrt[3]], 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) gamma(3/4) * sqrt(2 * Pi) * (3^(1/2)-1) / gamma(7/12) / gamma(2/3)
(PARI) 2^(1/4)*3^(3/8)/sqrt(1+sqrt(3)) \\ Charles R Greathouse IV, Jul 12 2026
(PARI) polrootsreal(x^8 + 18*x^4 - 27)[2] \\ Charles R Greathouse IV, Jul 12 2026

Crossrefs

Cf. A139137.

Sequence in context: A395946 A029684 A200626 * A360166 A197732 A224237

Adjacent sequences: A388643 A388644 A388645 * A388647 A388648 A388649

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved