Type: Article

On the sum of digits of some sequences of integers

Cilleruelo, Javier; Luca, Florian; Rue, Juanjo; et al.;

Abstract:

Let b a parts per thousand yen 2 be a fixed positive integer. We show for a wide variety of sequences {a (n) } (n=1) (a) that for almost all n the sum of digits of a (n) in base b is at least c (b) log n, where c (b) is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.