This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356022 #37 Mar 23 2025 03:20:45
%S A356022 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 A356022 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 A356022 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A356022 Decimal expansion of the infinite series Sum_{j>=0} 1/2^^j where ^^ indicates tetration.
%C A356022 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 A356022 This sequence has been inspired by a question posted by the user Max Muller on MathOverflow on July 2022 (see Links).
%H A356022 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=1..oo} 1/2^^n</a>, July 23 2022.
%F A356022 Equals Sum_{j>=0} 1/A014221(j).
%e A356022 1.812515258789...
%t A356022 RealDigits[Total[1/NestList[2^# &, 1, 5]], 10, 100][[1]] (* _Amiram Eldar_, Jul 23 2022 *)
%Y A356022 Cf. A014221, A356023, A007404.
%K A356022 nonn,cons
%O A356022 1,2
%A A356022 _Marco Ripà_, Jul 23 2022