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 A225053 #19 Feb 16 2025 08:33:19 %S A225053 1,6,9,4 %N A225053 Second terms of continued fractions for power towers e, e^e, e^e^e, ... %C A225053 It was conjectured (but remains unproved) that none of the power towers e, e^e, e^e^e, ... are integers. If so, the corresponding continued fractions contain at least 2 terms. If the conjecture fails, let the corresponding a(n) = 0. %H A225053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/e.html">e.</a> %H A225053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a> %H A225053 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration#Open_questions">Tetration, Open questions</a> %e A225053 a(3) = 9 because floor(1/frac(e^e^e)) = 9, since e^e^e ~ 3814279.10476. %t A225053 $MaxExtraPrecision = Infinity; terms = 4; Map[Function[x, ContinuedFraction[x, 2][[2]]], NestList[Exp, E, terms - 1]] %Y A225053 Cf. A003417, A064107, A159825, A225064, A004002. %Y A225053 A056072 yields the first term of the continued fraction. %K A225053 nonn,hard,more %O A225053 1,2 %A A225053 _Vladimir Reshetnikov_, Apr 25 2013