On the Gap sequence and the Gilbreath conjecture

Abstract

Motivated by the Gilbreath conjecture, we develop the notion of the gap sequence induced by any sequence of numbers. We introduce the notion of the path and associated circuits induced by an originator and study the conjecture via the notion of the trace and length of a path.

arXiv comment13 pages; the paper has been reformatted and introduction expanded; ideas remain unchanged; visuals of the trace, paths and circuit with paths supplied