For every positive integer let be the largest prime number . Given a positive integer , we study the positive integer such that if we define recursively for , then is a prime or . We obtain upper bounds for as well as an estimate for the set of whose takes on a fixed value .
Soit un nombre entier positif et le plus grand nombre premier . On considère la suite finie décroissante définie récursivement par , et dont le dernier terme, , est soit premier soit égal à . On note la longueur de cette suite. Nous obtenons des majorations pour ainsi qu’une estimation du nombre d’éléments de l’ensemble des en lesquels prend une valeur donnée .
@article{JTNB_2009__21_3_695_0, author = {Florian Luca and Ravindranathan Thangadurai}, title = {On an arithmetic function considered by {Pillai}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {695--701}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {3}, year = {2009}, doi = {10.5802/jtnb.695}, mrnumber = {2605540}, zbl = {1201.11092}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.695/} }
TY - JOUR AU - Florian Luca AU - Ravindranathan Thangadurai TI - On an arithmetic function considered by Pillai JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 695 EP - 701 VL - 21 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.695/ DO - 10.5802/jtnb.695 LA - en ID - JTNB_2009__21_3_695_0 ER -
%0 Journal Article %A Florian Luca %A Ravindranathan Thangadurai %T On an arithmetic function considered by Pillai %J Journal de théorie des nombres de Bordeaux %D 2009 %P 695-701 %V 21 %N 3 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.695/ %R 10.5802/jtnb.695 %G en %F JTNB_2009__21_3_695_0
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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