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A248042
Denominators of approximation to 2^(1/3) by Newton's method after n iterations.
3
1, 3, 72, 894348, 1703358734191174242
OFFSET
0,2
COMMENTS
Numerators are given in A248041.
LINKS
Eric Weisstein's World of Mathematics, Cube Root
Wikipedia, Cube Root
FORMULA
a(n) = y(n)/gcd(x(n),y(n))
where x(n) = 2*(A248041(n-1)^3*a(n-1)^2 + a(n-1)^5)
and y(n) = 3*A248041(n-1)^2*a(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: A135866 A307925 A006270 * A139888 A271628 A079594
KEYWORD
nonn,frac
AUTHOR
Kival Ngaokrajang, Jan 11 2015
STATUS
approved