A273918 - OEIS

%I #7 Jun 05 2016 23:52:51

%S 1,5,29,905,835409,698981939105,488580362881004355588929,

%T 238710771078004490460834598457103704776369419905

%N Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1.

%C a(8) is approximately 5.698 * 10^93.

%C The denominator of z(n) is 2^(2^n) for n > 0.

%C Given that the iteration of z(n) escapes to infinity, this shows that 1 is not in the Julia set for the function z^2 + 1/4. This is of course also true of -1.

%e 1^2 + 1/4 = 5/4, hence a(1) = 5.

%e (5/4)^2 + 1/4 = 25/16 + 4/16 = 29/16, hence a(2) = 29.

%t Numerator[NestList[#^2 + 1/4 &, 1, 8]]

%Y Cf. A015701, A020773.

%K easy,nonn

%O 0,2

%A _Alonso del Arte_, Jun 04 2016