A388113 - OEIS

%I #10 Jul 10 2026 08:22:40

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

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

%U 4,1,9,8,3,1,6,4,7,9,5,8,6,8,2,4,4,8,2

%N Decimal expansion of (sqrt(2) * exp(Pi / 2) * Gamma(5/4) * sin(Pi / 8)) / Pi^(3/4).

%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} A003982(k) / exp(k*Pi).

%e 1.0000034873423562514070036054270424470...

%t First[RealDigits[(Sqrt[2]*Exp[Pi/2]*Gamma[5/4]*Sin[Pi/8])/Pi^(3/4), 10, 100]]

%o (PARI) (1/8) * 2^(3/4) * gamma(5/8) * exp(1/2 * Pi) / Pi^(1/4) / gamma(7/8)

%Y Cf. A003982.

%K nonn,cons,changed

%O 1,7

%A _Simon Plouffe_, Sep 15 2025