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%I #11 Mar 04 2019 21:11:52
%S 2,11,233,108497,23543191457,1108563727961872518977,
%T 2457827077905448997994482872789298261401217,
%U 12081827889770476116093110581355561229584727594431650162181251776430351279198649072897
%N Numerators of rational approximations to sqrt(7) obtained from Newton's method.
%H R. Parimala, <a href="https://doi.org/10.1090/S0273-0979-2014-01443-0">A Hasse principle for quadratic forms over function fields</a>, Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 3, 447--461. MR3196794.
%e 2, 11/4, 233/88, 108497/41008, 23543191457/8898489952, ...
%p N:=7;
%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. A244013 (denominators).
%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
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