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 A356810 #31 Oct 01 2022 01:17:58
%S A356810 1,8,4,4,1,6,2,9,7,4,9,0,1,6,0,9,2,5,8,5,2,9,3,4,7,2,0,8,8,4,8,0,6,3,
%T A356810 2,5,5,5,8,0,4,7,6,6,4,5,6,4,4,5,0,9,0,7,1,3,9,8,0,4,3,8,3,0,2,7,5,0,
%U A356810 8,0,2,1,1,3,9,1,5,8,0,9,5,8,3,8,4,2,1,8,9,1,8,7,8,6,0,3,1,7
%N A356810 Decimal expansion of the unique root of the equation x^(x^(((log(x))^(x-1) - 1)/(log(x) - 1))) = x+1 for x in the interval [1,2].
%C A356810 This constant arises from a different interpretation of the equation x^^x = x+1, where x^^x indicates the tetration on the base x having the same height.
%C A356810 The alternative way to define x^^x is described by Takeji Ueda in his paper on Arxiv (see link below).
%C A356810 This definition implies that if Im(x) != 0, x cannot be a solution.
%C A356810 There are no other real solutions (conjecture).
%H A356810 Takeji Ueda, <a href="https://arxiv.org/abs/2105.00247">Extension of tetration to real and complex heights</a>, arXiv:2105.00247 [math.CA], 2021.
%e A356810 1.8441629749016...
%t A356810 RealDigits[x /. FindRoot[x^(x^(((Log[x])^(x - 1) - 1)/(Log[x] - 1))) == x + 1, {x,2}, WorkingPrecision -> 100]] [[1]]
%o A356810 (PARI) solve(x=3/2, 2, x^(x^(((log(x))^(x-1) - 1)/(log(x) - 1))) - x - 1) \\ _Michel Marcus_, Aug 29 2022
%Y A356810 Cf. A356805.
%K A356810 cons,nonn
%O A356810 1,2
%A A356810 _Flavio Niccolò Baglioni_ and _Marco Ripà _, Aug 29 2022