

A219164


Recurrence equation a(n+1) = a(n)^4  4*a(n)^2 + 2 with a(0) = 5.


3




OFFSET

0,1


COMMENTS

Bisection of A003487.
The next term  a(4)  has 175 digits.  Harvey P. Dale, Jun 09 2017


LINKS

Table of n, a(n) for n=0..3.


FORMULA

Let alpha = 1/2*(5 + sqrt(21)). Then a(n) = (alpha)^(4^n) + (1/alpha)^(4^n).
a(n) = A003487(2*n) = A003501(4^n).
Product {n = 0..inf} ((1 + 2/a(n))/(1  2/a(n)^2)) = sqrt(7/3).


MATHEMATICA

NestList[#^44#^2+2&, 5, 5] (* Harvey P. Dale, Jun 09 2017 *)


CROSSREFS

Cf. A001999, A003487, A003501, A219162, A219163, A219165.
Sequence in context: A283632 A270963 A110721 * A067446 A249895 A241325
Adjacent sequences: A219161 A219162 A219163 * A219165 A219166 A219167


KEYWORD

nonn,easy


AUTHOR

Peter Bala, Nov 13 2012


STATUS

approved



