%I #24 Jun 23 2023 23:27:05

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

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

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

%N Decimal expansion of Sum_{k>=0} 1/(k!)!.

%C The sum has 18 8's in a row within the first 23 decimal places.

%C 1801/720 approximates this constant to 23 significant digits.

%e 2.5013888888888888888888905006...

%p evalf(sum(1/(k!)!, k=0..infinity), 112); # _Alois P. Heinz_, Nov 20 2020

%t RealDigits[Sum[1/(k!)!, {k, 0, 4}], 10, 100][[1]] (* _Amiram Eldar_, Nov 21 2020 *)

%o (PARI) suminf(k=0, 1/(k!)!)

%Y Cf. A000197, A336810.

%K nonn,cons

%O 1,1

%A _Daniel Hoyt_, Nov 20 2020