Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus and by its powers , which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers.
We are interested whether there is a nonnegative integer and an infinite sequence of digits in base such that the numbers where are all prime or at least do not have prime divisors in a finite set of prime numbers If any such sequence contains infinitely many elements divisible by at least one prime number then we call the set unavoidable with respect to . It was proved earlier that unavoidable sets in base exist if and that no unavoidable set exists in base Now, we prove...