A388384 Decimal expansion of ((-1+sqrt(3)) * sqrt(Pi / 3) * exp(Pi / 4) * Gamma(11/12)) / (Gamma(2/3) * Gamma(3/4)).

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

Offset

1,3

Links

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

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

Formula

Empirical: Equals Sum_{k>=0} A036018(k) / exp(k*Pi).

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

Example

1.0451695080427296338943119880133221785...

Mathematica

First[RealDigits[((-1 + Sqrt[3])*Sqrt[Pi/3]*Exp[Pi/4]*Gamma[11/12])/(Gamma[2/3]*Gamma[3/4]), 10, 100]]
RealDigits[2^(1/4) * E^(Pi/4) / (3^(3/8) * (1 + Sqrt[3])^(1/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) 1/3 * exp(Pi / 4) * sqrt(Pi) * 3^(1/2) * gamma(11/12) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)

Crossrefs

Cf. A036018.

Sequence in context: A069284 A272638 A388890 * A365464 A299630 A068447

Adjacent sequences: A388381 A388382 A388383 * A388385 A388386 A388387

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved