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Numerators of rational approximations to sqrt(6) obtained from Newton's method.
4

%I #9 Jun 19 2014 17:19:47

%S 2,5,49,4801,46099201,4250272665676801,

%T 36129635465198759610694779187201,

%U 2610701117696295981568349760414651575095962187244375364404428801

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

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

%p N:=6;

%p s:=[floor(sqrt(N))];

%p M:=8;

%p for n from 1 to M do

%p x:=s[n];

%p h:=(N-x^2)/(2*x);

%p s:=[op(s),x+h]; od:

%p lprint(s);

%p s1:=map(numer,s);

%p s2:=map(denom,s);

%Y Cf. A244015, A084765.

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

%K nonn,frac

%O 0,1

%A _N. J. A. Sloane_, Jun 18 2014