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

1, 5, 29, 905, 835409, 698981939105, 488580362881004355588929, 238710771078004490460834598457103704776369419905

Offset: 0

Author

Alonso del Arte, Jun 04 2016

Keywords

• easy
• nonn

Comments

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

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

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.

Examples

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

Crossrefs

Cf. A015701, A020773.

Programs

Mathematica

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