The integer recurrence P(n)=a+P(n-phi(a)) I
Number Theory
2014-02-05 v3
Abstract
We prove that for a positive integer a the integer sequence P(n) satisfying for all n, -infty<n<infty, the recurrence P(n)=a+P(n-phi(a)), phi(a) the Euler function, generates in increasing order all integers P(n) coprime to a.The finite Fourier expansion of P(n) is given in terms of a, n, and the phi(a)-th roots of unity. Properties of the sequence are derived.
Cite
@article{arxiv.1208.5348,
title = {The integer recurrence P(n)=a+P(n-phi(a)) I},
author = {Constantin M. Petridi},
journal= {arXiv preprint arXiv:1208.5348},
year = {2014}
}
Comments
6 pages