A244015 Denominators of rational approximations to sqrt(6) obtained from Newton's method.

1, 2, 20, 1960, 18819920, 1735166549767840, 14749861913749949808286047759680, 1065814268211609269094400465471990022332221793124358274759711360

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Example

2, 5/2, 49/20, 4801/1960, 46099201/18819920, ...

Maple

N:=6;
s:=[floor(sqrt(N))];
M:=8;
for n from 1 to M do
x:=s[n];
h:=(N-x^2)/(2*x);
s:=[op(s), x+h]; od:
lprint(s);
s1:=map(numer, s);
s2:=map(denom, s);

Prog

(Magma) m:=9; f:=[n eq 1 select 2 else (Self(n-1)+6/Self(n-1))/2: n in [1..m]]; [Denominator(f[n]): n in [1..m]]; // Vincenzo Librandi, Jan 12 2016

Crossrefs

Cf. A244014 (numerators).

The analogs for sqrt(k), k=2,3,5,6,7 are: A001601/A051009, A002812/A071579, A081459/A081460, A244014/A244015, A244012/A244013.

Sequence in context: A263417 A053848 A347608 * A279691 A319639 A134476

Adjacent sequences: A244012 A244013 A244014 * A244016 A244017 A244018

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 18 2014

Status

approved