A244012 Numerators of rational approximations to sqrt(7) obtained from Newton's method.

2, 11, 233, 108497, 23543191457, 1108563727961872518977, 2457827077905448997994482872789298261401217, 12081827889770476116093110581355561229584727594431650162181251776430351279198649072897

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, 447--461. 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:=(N-x^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 A343898 A134096

Adjacent sequences: A244009 A244010 A244011 * A244013 A244014 A244015

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 18 2014

Status

approved