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 A225153 #13 Jul 07 2024 10:16:03
%S A225153 1,2,4,5,1,1,184,1,1,8,1,7,1,12,3,1,4,2,1,2,1,125,1,2,1,1,2,2,5,12,7,
%T A225153 1,8,2,1,6,1,3,2,1,2,1,14,1,1,1,3,1,1,6485,1,1,1,3,1,2,1,1,1,17,1,2,3,
%U A225153 3,3,2,7,1,2,1,8,1,9,1,1,7,1,4,9,1,1,1,1,3,2
%N A225153 Continued fraction for the positive root of x^x^x^x = 2 (A225134).
%C A225153 x = 1.44660143242986417... = 1 + 1/(2 + 1/(4 + 1/(5 + 1/(1 + 1/(1 + 1/(184 + 1/(...))))))).
%C A225153 This constant is sometimes called the 4th super-root of 2.
%C A225153 It is unknown if it is rational, algebraic irrational, or transcendental. Hence, it is unknown if this continued fraction is aperiodic, or even if it is infinite.
%H A225153 J. Marshall Ash and Yiren Tan, <a href="http://condor.depaul.edu/mash/atotheamg.pdf">A rational number of the form a^a with a irrational</a>, Mathematical Gazette 96, March 2012, pp. 106-109.
%H A225153 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration#Open_questions">Tetration, Open questions</a>
%H A225153 Wikipedia, <a href="http://en.wikipedia.org/wiki/Super-root">Super-root</a>
%t A225153 ContinuedFraction[FindRoot[x^x^x^x == 2, {x, 1}, WorkingPrecision -> 110][[1, 2]], 105]
%Y A225153 Cf. A225134 (decimal expansion), A225208 (Engel expansion), A153510 (second super-root of 2).
%K A225153 nonn,cofr,easy
%O A225153 0,2
%A A225153 _Vladimir Reshetnikov_, Apr 30 2013
%E A225153 Offset changed by _Andrew Howroyd_, Jul 07 2024