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 A280918 #9 Feb 16 2025 08:33:39
%S A280918 1,2,4,6,9,13,20,29,42,61,88,128,184,267,385,556,803,1159,1672,2413,
%T A280918 3481,5023,7247,10456,15085,21764,31399,45299,65354,94286,136026,
%U A280918 196245,283122,408459,589282,850155,1226515,1769487,2552830,3682956,5313383,7665592
%N A280918 2nd term of the continued fraction for 2-sqrt(2)^^n, where x^^n denotes tetration.
%C A280918 Tetration x^^n is defined recursively: x^^0 = 1, x^^n = x^(x^^(n-1)). Note that lim_{n->inf} sqrt(2)^^n = 2. This sequence shows the speed of convergence to this limit.
%H A280918 G. C. Greubel, <a href="/A280918/b280918.txt">Table of n, a(n) for n = 1..300</a>
%H A280918 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H A280918 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F A280918 a(n) ~ 1/(A277435*log(2)^n).
%t A280918 Table[ContinuedFraction[2 - Power@@Table[Sqrt[2], {n}], 2][[2]], {n, 42}]
%Y A280918 Cf. A198094, A277435.
%K A280918 nonn
%O A280918 1,2
%A A280918 _Vladimir Reshetnikov_, Jan 10 2017