A388396 - OEIS

%I #11 Jul 10 2026 13:14:49

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

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

%U 3,4,5,0,6,1,8,4,6,5,2,5,0,4,9,5,1,5,0

%N Decimal expansion of (1024 * (-4+3 * sqrt(2)) * exp(3 * Pi) * Gamma(5/4)^16) / Pi^12.

%H Simon Plouffe, <a href="https://plouffe.fr/articles/numbers%20in%20the%20base_exp_english%202025.pdf">Numbers in the base e^Pi</a>, 2025.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Empirical: Equals Sum_{k>=0} A034433(k) / exp(k*Pi).

%e 0.69140340250013819567554280455834592263...

%t First[RealDigits[(1024*(-4 + 3*Sqrt[2])*Exp[3*Pi]*Gamma[5/4]^16)/Pi^12, 10, 100]]

%o (PARI) (1/4194304) * exp(3 * Pi) * sqrt(2) * gamma(5/8)^16 * (99+70 * sqrt(2)) / Pi^4 / gamma(7/8)^16

%Y Cf. A034433.

%K nonn,cons

%O 0,1

%A _Simon Plouffe_, Sep 15 2025