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 A244013 #11 Mar 04 2019 23:12:07 %S A244013 1,4,88,41008,8898489952,418997705236253480128, %T A244013 928971316248341903257187589777603944778112, %U A244013 4566501711345281867283814391125123371716411674583075407993026856131137508750543524608 %N A244013 Denominators of rational approximations to sqrt(7) obtained from Newton's method. %H A244013 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 A244013 2, 11/4, 233/88, 108497/41008, 23543191457/8898489952, ... %p A244013 N:=7; %p A244013 s:=[floor(sqrt(N))]; %p A244013 M:=8; %p A244013 for n from 1 to M do %p A244013 x:=s[n]; %p A244013 h:=(N-x^2)/(2*x); %p A244013 s:=[op(s),x+h]; od: %p A244013 lprint(s); %p A244013 s1:=map(numer,s); %p A244013 s2:=map(denom,s); %Y A244013 Cf. A244012 (numerators). %Y A244013 The analogs for sqrt(k), k=2,3,5,6,7 are: A001601/A051009, A002812/A071579, A081459/A081460, A244014/A244015, A244012/A244013. %K A244013 nonn,frac %O A244013 0,2 %A A244013 _N. J. A. Sloane_, Jun 18 2014