|
%I #16 Mar 05 2019 01:48:27
%S 1,2,13,493,735853,1619459312173,7875984855578888541679213,
%T 186030029004437379749629399827828117533654561726893
%N 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
%C For root of c: f(n) = (1+c)*f(n-1)/(f(n-1)^2+1).
%C a(9) has 102 digits. - _Emeric Deutsch_, Jul 29 2009
%p 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
%o (PARI) f(n) = if (n==1, 1, 3*f(n-1)/(f(n-1)^2+1));
%o a(n) = denominator(f(n)); \\ _Michel Marcus_, Mar 04 2019
%Y Cf. A002193 (sqrt(2)), A163261 (numerators).
%Y Cf. A001601 and A051009: Newton's method.
%K nonn,frac
%O 1,2
%A _Mark Dols_, Jul 23 2009
%E a(7) and a(8) from _Emeric Deutsch_, Jul 29 2009
%E Name edited by _Michel Marcus_, Mar 04 2019
| 