A388492 Decimal expansion of (2/3) * exp(Pi / 12) * Pi^(1/3) * 3^(11/12) * Gamma(11/12)^(2/3) / Gamma(2/3)^(2/3) / Gamma(3/4)^(2/3) / (sqrt(2) * (1+3^(1/2)))^(2/3).

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

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} A098884(k) / exp(k*Pi).

Equals 2^(1/6) * exp(Pi/12) / (1 + sqrt(3))^(1/3). - Vaclav Kotesovec, Jan 08 2026

Example

1.0432140757715013973184249670107425800...

Mathematica

First[RealDigits[(Pi^(1/3)*Exp[Pi/12]*(((-1 + Sqrt[3])*Gamma[11/12])/(Gamma[2/3]*Gamma[3/4]))^(2/3))/3^(1/12), 10, 100]]
RealDigits[2^(1/6) * E^(Pi/12) / (1 + Sqrt[3])^(1/3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A098884.

Sequence in context: A093580 A196535 A388476 * A106655 A105313 A085064

Adjacent sequences: A388489 A388490 A388491 * A388493 A388494 A388495

Keyword

nonn,cons

Author

Simon Plouffe, Sep 17 2025

Status

approved