On an arithmetic function considered by Pillai
Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 695-701.

Soit n un nombre entier positif et p(n) le plus grand nombre premier pn. On considère la suite finie décroissante définie récursivement par n 1 =n, n i+1 =n i -p(n i ) et dont le dernier terme, n r , est soit premier soit égal à 1. On note R(n)=r la longueur de cette suite. Nous obtenons des majorations pour R(n) ainsi qu’une estimation du nombre d’éléments de l’ensemble des nx en lesquels R(n) prend une valeur donnée k.

For every positive integer n let p(n) be the largest prime number pn. 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 i1, 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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DOI : https://doi.org/10.5802/jtnb.695
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Florian Luca; Ravindranathan Thangadurai. On an arithmetic function considered by Pillai. Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 695-701. doi : 10.5802/jtnb.695. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.695/

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