

A244012


Numerators of rational approximations to sqrt(7) obtained from Newton's method.


4



2, 11, 233, 108497, 23543191457, 1108563727961872518977, 2457827077905448997994482872789298261401217, 12081827889770476116093110581355561229584727594431650162181251776430351279198649072897
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


LINKS

Table of n, a(n) for n=0..7.
R. Parimala, A Hasse principle for quadratic forms over function fields, Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 3, 447461. MR3196794.


EXAMPLE

2, 11/4, 233/88, 108497/41008, 23543191457/8898489952, ...


MAPLE

N:=7;
s:=[floor(sqrt(N))];
M:=8;
for n from 1 to M do
x:=s[n];
h:=(Nx^2)/(2*x);
s:=[op(s), x+h]; od:
lprint(s);
s1:=map(numer, s);
s2:=map(denom, s);


CROSSREFS

Cf. A244013 (denominators).
The analogs for sqrt(k), k=2,3,5,6,7 are: A001601/A051009, A002812/A071579, A081459/A081460, A244014/A244015, A244012/A244013.
Sequence in context: A088639 A269710 A162385 * A264330 A134096 A132571
Adjacent sequences: A244009 A244010 A244011 * A244013 A244014 A244015


KEYWORD

nonn,frac


AUTHOR

N. J. A. Sloane, Jun 18 2014


STATUS

approved



