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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
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OFFSET
0,2
COMMENTS
Numerators are given in
A248041
.
LINKS
Table of n, a(n) for n=0..4.
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
Cf.
A002580
,
A248041
.
Sequence in context:
A135866
A307925
A006270
*
A139888
A271628
A079594
Adjacent sequences:
A248039
A248040
A248041
*
A248043
A248044
A248045
KEYWORD
nonn
,
frac
AUTHOR
Kival Ngaokrajang
, Jan 11 2015
STATUS
approved
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Last modified August 28 00:57 EDT 2024. Contains 375475 sequences. (Running on oeis4.)