Let A be a finite subset of N containing 0, and let f (n) denote the number of ways to write n in the form ∑εj2j, where εj∈A. We show that there exists a computable T = T(A) so that the sequence (f (n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed.
- Stern sequence
- digital representations
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics