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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 (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)

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

Cf. A002580, A248042.

Sequence in context: A024261 A337827 A129434 * A209984 A065574 A113252

Adjacent sequences: A248038 A248039 A248040 * A248042 A248043 A248044

KEYWORD

nonn,frac

AUTHOR

Kival Ngaokrajang, Jan 11 2015

STATUS

approved

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Last modified November 29 12:24 EST 2022. Contains 358424 sequences. (Running on oeis4.)