JP Journal of Algebra, Number Theory and Applications
Volume 19, Issue 2, Pages 155 - 163
(December 2010)
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RECURRENCES BASED ON THE GREATEST PRIME FACTOR FUNCTION
Mihai Caragiu
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in which every term
is recursively defined as the
maximum element of the finite set
where
represents the greatest prime factor
of x, while
and
are fixed positive integers for
A special case of the conjecture
follows from a general elementary result (making use of the existence of
arbitrarily large prime gaps) guaranteeing the ultimate periodicity of integer
sequences satisfying
under certain conditions fulfilled
by the function f. The conditions are
not overly restrictive, among the functions satisfying them being the Euler’s
phi function.