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

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.

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.

Received:
Published online:
DOI: 10.5802/jtnb.695
Florian Luca 1; Ravindranathan Thangadurai 2

1 Mathematical Institute UNAM, Ap. Postal 61-3 (Xangari), CP 58089 Morelia, Michoacán, Mexico
2 Harish-Chandra Research Institute Chhatnag Road, Jhunsi Allahabad 211 019, India
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Florian Luca; Ravindranathan Thangadurai. On an arithmetic function considered by Pillai. Journal de Théorie des Nombres de Bordeaux, Volume 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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