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 A182503 #15 Feb 16 2025 08:33:13
%S A182503 2,3,3,4,5,15,17,66,196,233,284,375,1613,2131,3574,14122,24171,49097,
%T A182503 56871,69361,193406,243145,289951,682749,14501588,21191773,121635191,
%U A182503 810759781,1292785381,136110231377,294401497761
%N A182503 Engel expansion of the Dottie number, A003957.
%C A182503 Dottie number = 1/2 + 1/2/3 + 1/2/3/3 + 1/2/3/3/4 + 1/2/3/3/4/5 + 1/2/3/3/4/5/15 +...
%H A182503 G. C. Greubel, <a href="/A182503/b182503.txt">Table of n, a(n) for n = 1..500</a>
%H A182503 Jean-Christophe Pain, <a href="https://arxiv.org/abs/2303.17962">An exact series expansion for the Dottie number</a>, arXiv:2303.17962 [math.NT], 2023.
%H A182503 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A182503 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DottieNumber.html">Dottie Number</a>
%H A182503 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t A182503 EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]} &, {Ceiling[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; z = FindRoot[x == Cos[x], {x, 1}, WorkingPrecision -> 10000][[1, -1]]; EngelExp[z, 30]
%Y A182503 Cf. A003957, A006784.
%K A182503 nonn,easy
%O A182503 1,1
%A A182503 _Ben Branman_, May 02 2012