A388230 - OEIS

%I #10 Jul 10 2026 08:48:11

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

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

%U 6,1,8,4,6,8,0,3,2,3,9,1,4,9,8,7,3,4,7

%N Decimal expansion of (1/4096) * exp(5*Pi/4) * Pi^(15/2) * 2^(3/4) / Gamma(3/4)^30.

%H Paolo Xausa, <a href="/A388230/b388230.txt">Table of n, a(n) for n = 0..10000</a>

%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} A010835(k) / exp(k*Pi).

%e 0.25060698510614829308978567529902843560890792059105136676473505415250618468....

%t First[RealDigits[Exp[5*Pi/4]*Pi^(15/2)*2^(3/4)/(4096*Gamma[3/4]^30), 10, 100]] (* _Paolo Xausa_, Sep 16 2025 *)

%o (PARI) (1/4096) * exp(5/4 * Pi) * Pi^(15/2) * 2^(3/4) / gamma(3/4)^30

%Y Cf. A010835.

%K nonn,cons,changed

%O 0,1

%A _Simon Plouffe_, Sep 15 2025