A163261 Numerators of fractions in the approximation of the square root of 2 by means of: f(n)= 3f(n-1)/(f(n-1)^2+1); with f(1)= 1.

1, 3, 18, 702, 1038258, 2292015792222, 11135478955084481409955218, 263108590829588406010634295716681354685770554450302

Offset: 1

Author

Mark Dols, Jul 23 2009

Keywords

• nonn
• frac

Comments

For root c: f(n) = (1+c)*f(n-1)/(f(n-1)^2+1).

Crossrefs

Cf. A002193 (sqrt(2)), A163262 (denominators).

Cf. A001601 and A051009: Newton's method.

Programs

PARI

f(n) = if (n==1, 1, 3*f(n-1)/(f(n-1)^2+1));
a(n) = numerator(f(n)); \\ Michel Marcus, Mar 05 2019

Formula

a(n+1) = 3*a(n)*A163262(n). - Philippe Deléham, Oct 11 2011

Extensions

More terms from Michel Marcus, Mar 05 2019