A244014 Numerators of rational approximations to sqrt(6) obtained from Newton's method.

2, 5, 49, 4801, 46099201, 4250272665676801, 36129635465198759610694779187201, 2610701117696295981568349760414651575095962187244375364404428801

Offset: 0

Author

N. J. A. Sloane, Jun 18 2014

Keywords

• nonn
• frac

Examples

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

Crossrefs

Cf. A244015, A084765.

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

Programs

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);