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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, 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 A134096 A132571

Adjacent sequences:  A244009 A244010 A244011 * A244013 A244014 A244015

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Jun 18 2014

STATUS

approved

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)