cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A273918 Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1.

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%I A273918 #7 Jun 05 2016 23:52:51
%S A273918 1,5,29,905,835409,698981939105,488580362881004355588929,
%T A273918 238710771078004490460834598457103704776369419905
%N A273918 Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1.
%C A273918 a(8) is approximately 5.698 * 10^93.
%C A273918 The denominator of z(n) is 2^(2^n) for n > 0.
%C A273918 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 A273918 1^2 + 1/4 = 5/4, hence a(1) = 5.
%e A273918 (5/4)^2 + 1/4 = 25/16 + 4/16 = 29/16, hence a(2) = 29.
%t A273918 Numerator[NestList[#^2 + 1/4 &, 1, 8]]
%Y A273918 Cf. A015701, A020773.
%K A273918 easy,nonn
%O A273918 0,2
%A A273918 _Alonso del Arte_, Jun 04 2016