Every non-negative integer n can be represented essentially uniquely in base 2, as follows:
n=∑ 0≤ i≤ j ei2i where ei∈{0, 1} and ej= 0 for n= 0. We consider the consequences of …

arXiv:2003.08083v3 [math.NT] 11 Nov 2020 Page 1 ADDITIVE REPRESENTATIONS OF
NATURAL NUMBERS FORREST J. FRANCIS AND ETHAN S. LEE Abstract. Every natural …

A double-base representation of an integer $ n $ is an expression $ n= n_1+\cdots+ n_r $,
where the $ n_i $ are (positive or negative) integers that are divisible by no primes other …

G untzer and Paul introduced a number system with base 2 and digits 1; 0; 1 which is
characterized by separating nonzero digits by at least one zero. We nd an explicit formula …

ON THE NUMBER OF NON-ZERO DIGITS OF INTEGERS IN MULTI-BASE REPRESENTATIONS
1. Introduction It is an old problem to study integer Page 1 ON THE NUMBER OF NON-ZERO …

Double Sequential Representations of Natural Numbers - II Page 1 Inder J. Taneja RGMIA
Research Report Collection, 19(2016), pp. 1-42, http://rgmia.org/v19.php Double Sequential …

In a multi-base representation, in contrast to the common b-ary representation, the base is
replaced by products of powers of single bases. The resulting numeral system has desirable …

Let b≥2 be an integer. Not much is known on the representation in base b of prime numbers
or of numbers whose prime factors belong to a given, finite set. Among other results, we …

It is known that every positive integer n can be represented as a finite sum of the form
n=\textstyle∑a_i2^i, where a_i∈{0,1,-1\} for all i, and no two consecutive ai's are nonzero …

We study representations of integers n in binary expansions using the digits 0,±1. We
analyze the average number of such representations of minimal “weight”(= number of non …