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%I #19 Aug 01 2019 00:16:16
%S 1,4,91,1126819,2146097524939083451
%N Numerators of approximation to 2^(1/3) by Newton's method after n iterations.
%C Denominators are given in A248042.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubeRoot.html">Cube Root</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cube_root">Cube Root</a>
%F a(n) = x(n)/gcd(x(n),y(n))
%F where x(n) = 2*(a(n-1)^3*A248042(n-1)^2 + A248042(n-1)^5)
%F and y(n) = 3*a(n-1)^2*A248042(n-1)^3;
%F x(0) = y(0) = 1.
%e Approximations to 2^(1/3):
%e n = 1: 4/3 = 1.33333...; error = 0.07341...
%e n = 2: 91/72 = 1.26388...; error = 0.00396...
%e n = 3: 1126819/894348 = 1.25993...; error = 0.00001...
%e ...
%Y Cf. A002580, A248042.
%K nonn,frac
%O 0,2
%A _Kival Ngaokrajang_, Jan 11 2015
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