A389046 - OEIS

A389046

Decimal expansion of (-4 * sqrt(6 * (2-sqrt(2)) * (2-sqrt(3))) * Gamma(3/4)^8) / (Pi^(1/4) * Gamma(-1/3) * Gamma(7/12)^3 * Gamma(11/12)^2).

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..86.

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

FORMULA

Empirical: Equals Sum_{k>=0} A320070(k) / exp(k*Pi).

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

EXAMPLE

0.91686885321840156196523961718337655130...

MATHEMATICA

First[RealDigits[(-4*Sqrt[6*(2 - Sqrt[2])*(2 - Sqrt[3])]*Gamma[3/4]^8)/(Pi^(1/4)*Gamma[-1/3]*Gamma[7/12]^3*Gamma[11/12]^2), 10, 100]]

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

PROG

(PARI) (32/9) * Pi^(15/4) * 3^(1/2) * gamma(7/8)^8 * (2-2^(1/2))^(1/2) / (1+3^(1/2)) / gamma(5/8)^8 / gamma(7/12)^3 / (17/12+2^(1/2)) / gamma(11/12)^2 / gamma(2/3)

CROSSREFS

Cf. A320070.

Sequence in context: A363876 A195712 A389050 * A296473 A388613 A388874

Adjacent sequences: A389043 A389044 A389045 * A389047 A389048 A389049

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 22 2025

STATUS

approved