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A248041
Numerators of approximation to 2^(1/3) by Newton's method after n iterations.
3
1, 4, 91, 1126819, 2146097524939083451
OFFSET
0,2
COMMENTS
Denominators are given in A248042.
LINKS
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)
and y(n) = 3*a(n-1)^2*A248042(n-1)^3;
x(0) = y(0) = 1.
EXAMPLE
Approximations to 2^(1/3):
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
Sequence in context: A024261 A337827 A129434 * A209984 A113252 A003737
KEYWORD
nonn,frac
AUTHOR
Kival Ngaokrajang, Jan 11 2015
STATUS
approved