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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A248041 revision #12 A248041 Numerators of approximation of cuberoot(2) by Newton's method at n iterations. 3 1, 4, 91, 1126819, 2146097524939083451 (list; graph; refs; listen; history; text; internal format) OFFSET 0,2 COMMENTS Denominators are given in A248042. LINKS Table of n, a(n) for n=0..4. Eric Weisstein's World of Mathematics, Cube Root Wikipedia, Cube Root FORMULA a(n) = x(n)/GCD(x(n),y(n)). where x(n) = 2*(a(n-1)^3*A248042(n-1)^2 + A248042(n-1)^5); y(n) = 3*a(n-1)^2*A248042(n-1)^3; x(0) = y(0) = 1. EXAMPLE CubeRoot(2) approximations: n = 1: 4/3 = 1.33333...; error = 0.07341... n = 2: 91/72 = 1.26388...; error = 0.00396... n = 3: 1126819/894348 = 1.25993...; error = 0.00001... ... CROSSREFS Cf. A002580, A248042. Sequence in context: A024261 A337827 A129434 * A209984 A113252 A003737 Adjacent sequences: A248038 A248039 A248040 * A248042 A248043 A248044 KEYWORD nonn,frac AUTHOR Kival Ngaokrajang, Jan 11 2015 STATUS proposed

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Last modified August 31 19:25 EDT 2024. Contains 375573 sequences. (Running on oeis4.)