heathd@stolaf.UUCP (Daniel J. Heath) (02/28/84)
I recently encounterred this problem in the American Mathematics Monthly
(Feb 1984, Vol. 91, No. 2, Proposed by F. Lazebnik, Univ Pennsylvania and
Y. Pilipenko, Kiev Univ. USSR.):
Define a sequence {a[n]} (where [n] is a subscript--rather hard to
represent in type) such that a[1] = a and a[n+1] = a[n]^2-2. For what
values of a does this sequence converge.
It is with a fair amount of ease that I defined an infinite number
of values that fulfill these stipulations. Lately, with all this talk
of complex numbers, I came up with a similar, yet somewhat more difficult
problem which I would like to propose to you math-masochists like myself.
Given a sequence {a[n]} such that a[1] = a and a[n+1] = a[n]^2-2*i,
are there values such that this sequence converges, and if so, what are
they? Send any comments to me, I'll post them.
deej
!stolaf!heathd