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, 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

Links

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

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

Adjacent sequences: A163259 A163260 A163261 * A163263 A163264 A163265

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