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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
1, 3, 18, 702, 1038258, 2292015792222, 11135478955084481409955218, 263108590829588406010634295716681354685770554450302 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..8.

FORMULA

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

PROG

(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

CROSSREFS

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

Cf. A001601 and A051009: Newton's method.

Sequence in context: A304780 A265468 A070953 * A064846 A157544 A202946

Adjacent sequences:  A163258 A163259 A163260 * A163262 A163263 A163264

KEYWORD

nonn,frac

AUTHOR

Mark Dols, Jul 23 2009

EXTENSIONS

More terms from Michel Marcus, Mar 05 2019

STATUS

approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)