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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
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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
A113252
A003737
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 August 31 15:16 EDT 2024. Contains 375572 sequences. (Running on oeis4.)