This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A244012 #11 Mar 04 2019 21:11:52 %S A244012 2,11,233,108497,23543191457,1108563727961872518977, %T A244012 2457827077905448997994482872789298261401217, %U A244012 12081827889770476116093110581355561229584727594431650162181251776430351279198649072897 %N A244012 Numerators of rational approximations to sqrt(7) obtained from Newton's method. %H A244012 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 A244012 2, 11/4, 233/88, 108497/41008, 23543191457/8898489952, ... %p A244012 N:=7; %p A244012 s:=[floor(sqrt(N))]; %p A244012 M:=8; %p A244012 for n from 1 to M do %p A244012 x:=s[n]; %p A244012 h:=(N-x^2)/(2*x); %p A244012 s:=[op(s),x+h]; od: %p A244012 lprint(s); %p A244012 s1:=map(numer,s); %p A244012 s2:=map(denom,s); %Y A244012 Cf. A244013 (denominators). %Y A244012 The analogs for sqrt(k), k=2,3,5,6,7 are: A001601/A051009, A002812/A071579, A081459/A081460, A244014/A244015, A244012/A244013. %K A244012 nonn,frac %O A244012 0,1 %A A244012 _N. J. A. Sloane_, Jun 18 2014