A388925 Decimal expansion of ((-6+4 * sqrt(3)) * Pi * Gamma(11/12)^2) / (Gamma(2/3)^2 * Gamma(3/4)^2).

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

Formula

Empirical: Equals Sum_{k>=0} A261321(k) / exp(k*Pi).

Equals 3^(3/4) * (sqrt(3) - 1) / sqrt(2). - Vaclav Kotesovec, Jan 09 2026

Example

1.1799596795709859174936490058908063975...

Mathematica

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

Prog

(PARI) -2 * Pi * 3^(1/2) * gamma(11/12)^2 * (-2+3^(1/2)) / gamma(2/3)^2 / gamma(3/4)^2
(PARI) 3^(3/4)*(sqrt(3)-1)/sqrt(2) \\ Charles R Greathouse IV, Jul 13 2026
(PARI) polrootsreal(x^4 + 18*x^2 - 27)[2] \\ Charles R Greathouse IV, Jul 13 2026

Crossrefs

Cf. A261321.

Sequence in context: A198753 A244625 A363906 * A347218 A175642 A242612

Adjacent sequences: A388922 A388923 A388924 * A388926 A388927 A388928

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 21 2025

Status

approved