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A163262
Denominators of fractions in the approximation of the square root of 2 by means of: f(n) = 3*f(n-1)/(f(n-1)^2+1); with f(1)= 1
1
1, 2, 13, 493, 735853, 1619459312173, 7875984855578888541679213, 186030029004437379749629399827828117533654561726893
OFFSET
1,2
COMMENTS
For root of c: f(n) = (1+c)*f(n-1)/(f(n-1)^2+1).
a(9) has 102 digits. - Emeric Deutsch, Jul 29 2009
MAPLE
f[1] := 1: for n from 2 to 10 do f[n] := 3*f[n-1]/(1+f[n-1]^2) end do: seq(denom(f[n]), n = 1 .. 8); # Emeric Deutsch, Jul 29 2009
PROG
(PARI) f(n) = if (n==1, 1, 3*f(n-1)/(f(n-1)^2+1));
a(n) = denominator(f(n)); \\ Michel Marcus, Mar 04 2019
CROSSREFS
Cf. A002193 (sqrt(2)), A163261 (numerators).
Cf. A001601 and A051009: Newton's method.
Sequence in context: A082751 A120935 A015183 * A132570 A013048 A342958
KEYWORD
nonn,frac
AUTHOR
Mark Dols, Jul 23 2009
EXTENSIONS
a(7) and a(8) from Emeric Deutsch, Jul 29 2009
Name edited by Michel Marcus, Mar 04 2019
STATUS
approved