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arXiv · 1208.5348

The integer recurrence P(n)=a+P(n-phi(a)) I

Constantin M. Petridi
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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.

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Constantin M. Petridi. 2012-08-27. The integer recurrence P(n)=a+P(n-phi(a)) I. https://arxiv.org/abs/1208.5348

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