A388929 Decimal expansion of Pi^(5/4) * 3^(1/4) * Gamma(11/12) * (3^(1/2)-1) / Gamma(2/3) / Gamma(3/4)^4.

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

Offset

1,2

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} A261394(k) / exp(k*Pi).

Equals 3^(3/8) * Gamma(1/4)^3 / (2^(5/4) * sqrt(1 + sqrt(3)) * Pi^(9/4)). - Vaclav Kotesovec, Jan 09 2026

Example

1.3929791042022874617110949187750262205...

Mathematica

First[RealDigits[(3^(1/4)*(-1 + Sqrt[3])*Pi^(5/4)*Gamma[11/12])/(Gamma[2/3]*Gamma[3/4]^4), 10, 100]]
RealDigits[3^(3/8)*Gamma[1/4]^3 / (2^(5/4)*Sqrt[1 + Sqrt[3]]*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

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

Crossrefs

Cf. A261394.

Sequence in context: A125301 A386689 A347214 * A263559 A262343 A140985

Adjacent sequences: A388926 A388927 A388928 * A388930 A388931 A388932

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved