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 A356805 #13 Sep 05 2022 09:10:16
%S A356805 1,8,5,5,6,6,0,2,3,1,9,6,1,7,3,1,1,1,2,6,7,8,8,3,9,3,7,4,4,4,3,4,8,0,
%T A356805 8,7,7,9,0,3,4,8,4,1,9,2,8,0,0,3,4,4,9,5,5,1,8,0,8,8,5,2,3,4,5,2,8,5,
%U A356805 5,9,6,7,9,7,3,8,7,3,8,5,8,3,4,7,4,8,9
%N A356805 Decimal expansion of the unique positive real root of the equation x^x^(x - 1) = x + 1.
%C A356805 This constant arises from a well-known linear approximation for real height of the tetration x^^x (for x belonging to (1, 2)), where x^^x indicates the tetration of the real base x having the same height (see Links - Wikipedia).
%C A356805 A valuable method to extend tetration to real numbers, and solving equations as the above, has been introduced in 2006 by Hooshmand in his paper "Ultra power and ultra exponential functions" (see Links - Hooshmand).
%H A356805 Mohammad Hadi Hooshmand, <a href="https://doi.org/10.1080/10652460500422247">Ultra power and ultra exponential functions</a>, Integral Transforms and Special Functions, Volume 17(8), 2006, pp. 549-558.
%H A356805 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration#Real_heights">Tetration</a> (see in particular "Linear approximation for real heights").
%e A356805 1.85566023196173...
%t A356805 RealDigits[x /. FindRoot[x^(x^(x - 1)) == x + 1, {x, 2}, WorkingPrecision -> 100]][[1]]
%o A356805 (PARI) solve(x=1, 2, x^x^(x - 1) - x - 1) \\ _Michel Marcus_, Aug 29 2022
%Y A356805 Cf. A124930, A356562.
%K A356805 cons,nonn
%O A356805 1,2
%A A356805 _Marco Ripà _ and _Flavio Niccolò Baglioni_, Aug 28 2022