A388759 - OEIS

A388759

Decimal expansion of (1/24) * exp(17*Pi/24) * Pi^(5/4) * 2^(5/8) * 3^(1/2) * Gamma(11/12) * (3^(1/2)-1) / Gamma(2/3) / Gamma(3/4)^4.

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

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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 transcendental numbers.

FORMULA

Empirical: Equals Sum_{k>=0} A213023(k) / exp(k*Pi).

Equals exp(17*Pi/24) * Gamma(1/4)^3 / (2^(29/8) * 3^(3/8) * sqrt(1 + sqrt(3)) * Pi^(9/4)). - Vaclav Kotesovec, Jan 08 2026

EXAMPLE

1.09041212386967517556845468792454414338504922209761020298377263753555053717....

MATHEMATICA

First[RealDigits[-1/12*((-3 + Sqrt[3])*Pi^(5/4)*Exp[(17*Pi)/24]*Gamma[11/12])/(2^(3/8)*Gamma[2/3]*Gamma[3/4]^4), 10, 100]]

RealDigits[E^(17*Pi/24) * Gamma[1/4]^3 / (2^(29/8)*3^(3/8)*Sqrt[1 + Sqrt[3]]*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

PROG

(PARI) (1/24) * exp(17/24 * Pi) * Pi^(5/4) * 2^(5/8) * 3^(1/2) * gamma(11/12) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)^4

(PARI) exp(17*Pi/24)*gamma(1/4)^3/(2^(29/8)*3^(3/8)*sqrt(1+sqrt(3))*Pi^(9/4)) \\ Charles R Greathouse IV, Jul 13 2026

CROSSREFS

Cf. A213023.

Sequence in context: A094452 A154705 A197389 * A086307 A215141 A248951

Adjacent sequences: A388756 A388757 A388758 * A388760 A388761 A388762

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 18 2025

STATUS

approved