The Hurt-Sada Array and Zeckendorf Representations
Abstract
Wesley Ivan Hurt and Ali Sada both independently proposed studying an infinite array where the 0th row consists of the nonnegative integers 0,1,2,… in increasing order. Thereafter the nth row is formed from the (n−1)’th row by “jumping” the single entry n by n places to the right. Sada also defined a sequence s(n) to be the first number that n jumps over. In this note I show how the Hurt-Sada array and Sada’s sequence are intimately connected with the golden ratio φ, the infinite Fibonacci word, and Zeckendorf representation. I also consider a number of related sequences.
Fields of Study & Subjects
Cellular Automata and Applications
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Pages
- 1–14
- Publication date
- 20 May 2026
- Language
- EN