Decomposition into weight * level + jump and application to a new classification of primes
Abstract
In this paper we introduce an Euclidean decomposition of elements a_n of an increasing sequence of natural numbers into weight * level + jump which we use to classify the numbers a_n either by weight or by level. We then show that this decomposition can be seen as a generalization of the sieve of Eratosthenes (which is the particular case of the whole sequence of natural numbers). We apply this decomposition to prime numbers in order to obtain a new classification of primes, we analyze a few properties of this classification and we make a series of conjectures based on numerical data. Finally we show how composite numbers and 2-almost primes behave under the decomposition.
Keywords
Cite
@article{arxiv.0711.0865,
title = {Decomposition into weight * level + jump and application to a new classification of primes},
author = {Remi Eismann},
journal= {arXiv preprint arXiv:0711.0865},
year = {2010}
}
Comments
Submitted to Journal of Integer Sequences October 8 2007, rejected December 30 2007 for not significant enough contribution and non-standard terminology. V2: introduction deleted, V3: table 6 added, conjecture 9 added, V4: minor corrections; 12 pages, 4 figures, 6 tables