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 A248041 #20 Feb 16 2025 08:33:23 %S A248041 1,4,91,1126819,2146097524939083451 %N A248041 Numerators of approximation to 2^(1/3) by Newton's method after n iterations. %C A248041 Denominators are given in A248042. %H A248041 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubeRoot.html">Cube Root</a> %H A248041 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cube_root">Cube Root</a> %F A248041 a(n) = x(n)/gcd(x(n),y(n)) %F A248041 where x(n) = 2*(a(n-1)^3*A248042(n-1)^2 + A248042(n-1)^5) %F A248041 and y(n) = 3*a(n-1)^2*A248042(n-1)^3; %F A248041 x(0) = y(0) = 1. %e A248041 Approximations to 2^(1/3): %e A248041 n = 1: 4/3 = 1.33333...; error = 0.07341... %e A248041 n = 2: 91/72 = 1.26388...; error = 0.00396... %e A248041 n = 3: 1126819/894348 = 1.25993...; error = 0.00001... %e A248041 ... %Y A248041 Cf. A002580, A248042. %K A248041 nonn,frac %O A248041 0,2 %A A248041 _Kival Ngaokrajang_, Jan 11 2015