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

%I #13 Sep 08 2022 08:46:08

%S 1,2,20,1960,18819920,1735166549767840,

%T 14749861913749949808286047759680,

%U 1065814268211609269094400465471990022332221793124358274759711360

%N Denominators 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);

%o (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

%Y Cf. A244014 (numerators).

%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 0,2

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