A356023 - OEIS

%I #33 Dec 10 2023 09:27:28

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

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Decimal expansion of Sum_{j>=1} 2^^j/2^^(j+1) where ^^ indicates tetration.

%C This series converges quickly and a very good approximation of this constant is given by the first three terms, 2/2^2 + 2^2/2^2^2 + 2^2^2/2^2^2^2 = 3073/4096, since the next term 2^2^2^2/2^2^2^2^2 is about 1/10^19723.4853.

%e 0.750244140625...

%t RealDigits[Total[Most[(s = NestList[2^# &, 2, 4])]/Rest[s]], 10, 100][[1]] (* _Amiram Eldar_, Jul 23 2022 *)

%Y Cf. A356022.

%K nonn,cons

%O 0,1

%A _Marco Ripà_, Jul 23 2022