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.
Tribute to Jean Lavorel (16 March 1928–12 January 2021), a pioneer of the ‘Light Reactions of Photosynthesis’. He was known not only for his ingenuity in devising new instruments but in thoroughly analyzing all the available data theoretically and mathematically – mostly all by himself. He measured, elegantly, oxygen evolution and light given off by photosynthetic organisms, both prompt and delayed chlorophyll fluorescence. He ingeniously used these data to understand how light energy is converted to chemical energy in natural systems. We present below a summary of his life and research.