Luca, Thangadurai: On an arithmetic function considered by Pillai

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Florian Luca; Ravindranathan Thangadurai
On an arithmetic function considered by Pillai
Journal de théorie des nombres de Bordeaux, 21 no. 3 (2009), p. 695-701
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Résumé - Abstract

For every positive integer $n$ let $p(n)$ be the largest prime number $p\le n$. Given a positive integer $n=n_1$, we study the positive integer $r=R(n)$ such that if we define recursively $n_{i+1}=n_i-p(n_i)$ for $i\ge 1$, then $n_r$ is a prime or $1$. We obtain upper bounds for $R(n)$ as well as an estimate for the set of $n$ whose $R(n)$ takes on a fixed value $k$.

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