A389050 - OEIS

A389050

Decimal expansion of -(128/15) * (-3+3^(1/2)) * 10^(1/4) * (2-sqrt(2))^(9/2) * (5/2+5^(1/2)) * Pi^4 * Gamma(7/8)^9 / (2+sqrt(2))^(1/2) * (5-5^(1/2))^(3/2) / (5^(1/2)+1)^3 / Gamma(11/12)^2 / Gamma(7/12)^3 / Gamma(5/8)^9 / Gamma(2/3).

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

(list; constant; graph; refs; listen; history; text; internal format)

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} A320140(k) / exp(k*Pi).

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

EXAMPLE

0.91686857687104464057169857981769242737...

MATHEMATICA

First[RealDigits[(32*10^(1/4)*(-17 + 12*Sqrt[2])*(-3 + Sqrt[3])*Sqrt[(3 - 2*Sqrt[2])*(5 - Sqrt[5])]*(-1 + Sqrt[5])*Pi^4*Gamma[7/8]^9)/(3*Gamma[7/12]^3*Gamma[5/8]^9*Gamma[2/3]*Gamma[11/12]^2), 10, 100]]

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

PROG

(PARI) -(128/15) * (-3+3^(1/2)) * 10^(1/4) * (2-2^(1/2))^(9/2) * (5/2+5^(1/2)) * Pi^4 * gamma(7/8)^9 / (2+2^(1/2))^(1/2) * (5-5^(1/2))^(3/2) / (5^(1/2)+1)^3 / gamma(11/12)^2 / gamma(7/12)^3 / gamma(5/8)^9 / gamma(2/3)

CROSSREFS

Cf. A320140.

Sequence in context: A264934 A363876 A195712 * A389046 A296473 A388613

Adjacent sequences: A389047 A389048 A389049 * A389051 A389052 A389053

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 22 2025

STATUS

approved