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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.

%I A163262 #18 Jun 02 2025 01:48:00
%S A163262 1,2,13,493,735853,1619459312173,7875984855578888541679213,
%T A163262 186030029004437379749629399827828117533654561726893
%N 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.
%C A163262 For root of c: f(n) = (1+c)*f(n-1)/(f(n-1)^2+1).
%C A163262 a(9) has 102 digits. - _Emeric Deutsch_, Jul 29 2009
%p A163262 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 A163262 (PARI) f(n) = if (n==1, 1, 3*f(n-1)/(f(n-1)^2+1));
%o A163262 a(n) = denominator(f(n)); \\ _Michel Marcus_, Mar 04 2019
%Y A163262 Cf. A002193 (sqrt(2)), A163261 (numerators).
%Y A163262 Cf. A001601 and A051009: Newton's method.
%K A163262 nonn,frac
%O A163262 1,2
%A A163262 _Mark Dols_, Jul 23 2009
%E A163262 a(7) and a(8) from _Emeric Deutsch_, Jul 29 2009
%E A163262 Name edited by _Michel Marcus_, Mar 04 2019