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A273918 Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1. 0
1, 5, 29, 905, 835409, 698981939105, 488580362881004355588929, 238710771078004490460834598457103704776369419905 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..7.

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A015701, A020773.

Sequence in context: A263369 A072880 A112959 * A085553 A057208 A046842

Adjacent sequences:  A273915 A273916 A273917 * A273919 A273920 A273921

KEYWORD

easy,nonn

AUTHOR

Alonso del Arte, Jun 04 2016

STATUS

approved

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Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)