Unique Representation of Positive Integers as a Sum of Distinct Tribonacci Numbers
Salim Badidja, Abdelmadjid Boudaoud · Journal of Mathematics and Statistics · 2017
Let (Tm)m≥1 be the tribonacci sequence. We show that every integer N ≥ 1 can be written as a sum of the terms αm Tm, where m runs over the set of strictly positive integers and αm (m ≥ 1) are either 1 or 0. The previous representation of N is unique if each time that we have αm = 1 then at least the two coefficients directly following αm are zero, i.e., αm+1 = αm+2 = 0.