The Binary Enots Wolley Sequence

TL;DR

This paper proves a property of an analog of the Enots Wolley sequence, showing it is surjective onto positive integers with binary weight at least 2, by analyzing binary representations rather than prime factorizations.

Contribution

It introduces and proves a surjectivity property for a binary representation-based analog of the Enots Wolley sequence.

Findings

Proved the surjectivity of the binary-based sequence onto integers with binary weight ≥ 2.

Established a connection between the sequence's behavior and binary representations.

Extended understanding of sequence properties beyond prime factorization.

Abstract

It is an open conjecture that the Enots Wolley sequence is surjective onto the set of positive integers with a binary weight of at least 2. In this paper, this property is proved for an analog of the Enots Wolley sequence which operates on the binary representation of a number rather than the prime factorization.