Our previous research was devoted to the problem of determining the primitive periods of the sequences (Gn mod p t )∞ n=1 where (Gn)∞ n=1 is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime p ≠ 2, 11. In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes p = 2, 11.
Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus p and by its powers p t , 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.