Chain addition cycles Original Research Article

For each seed s=(s1,s2,…,sn) of elements si chosen from the ring image of integers modulo m, the infinite sequence image satisfying sn+k=sk+sk+1 (addition in image) for every positive integer k is the (m,n) chain addition sequence generated by the seed s. We investigate the maximal period, Ln(m), of chain addition cycles with seed length n (modulo m). The general problem is reduced to finding Ln(pk) for primes p and it is shown that if Ln(p2)≠Ln(p), then Ln(pk)=pk−1Ln(p) for positive integers k. Further, conditions guaranteeing that Ln(p2)≠Ln(p) are given.