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 A248042 #18 Feb 16 2025 08:33:23 %S A248042 1,3,72,894348,1703358734191174242 %N A248042 Denominators of approximation to 2^(1/3) by Newton's method after n iterations. %C A248042 Numerators are given in A248041. %H A248042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubeRoot.html">Cube Root</a> %H A248042 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cube_root">Cube Root</a> %F A248042 a(n) = y(n)/gcd(x(n),y(n)) %F A248042 where x(n) = 2*(A248041(n-1)^3*a(n-1)^2 + a(n-1)^5) %F A248042 and y(n) = 3*A248041(n-1)^2*a(n-1)^3; %F A248042 x(0) = y(0) = 1. %e A248042 Approximations to 2^(1/3): %e A248042 n = 1: 4/3 = 1.33333...; error = 0.07341... %e A248042 n = 2: 91/72 = 1.26388...; error = 0.00396... %e A248042 n = 3: 1126819/894348 = 1.25993...; error = 0.00001... %e A248042 ... %Y A248042 Cf. A002580, A248041. %K A248042 nonn,frac %O A248042 0,2 %A A248042 _Kival Ngaokrajang_, Jan 11 2015