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%I #33 Dec 10 2023 09:27:42
%S 1,8,1,2,5,1,5,2,5,8,7,8,9,0,6,2,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%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 the infinite series Sum_{j=0..oo} 1/2^^j where ^^ indicates tetration.
%C This constant converges very fast to a finite value around 118785/65536, since tetration (AKA hyper-4) makes 2^^k become very big so quickly, even for "relatively small" values of k (e.g., 1/2^^5 < 1/10^19728.30).
%C This sequence has been inspired by a question posted by the user Max Muller on MathOverflow on July 2022 (see Links).
%H MathOverflow, <a href="https://mathoverflow.net/questions/427049/references-on-infinite-series-involving-the-tetration-operator-like-sum-n-1">References on infinite series involving the tetration operator, like sum(n=0,infinity)1/2^^n</a>, July 23 2022.
%F Equals Sum_{j=0..oo) A014221(j).
%e 1.812515258789...
%t RealDigits[Total[1/NestList[2^# &, 1, 5]], 10, 100][[1]] (* _Amiram Eldar_, Jul 23 2022 *)
%Y Cf. A014221, A356023, A007404.
%K nonn,cons
%O 1,2
%A _Marco Ripà_, Jul 23 2022