Type: Article

On the fractional parts of a(n)/n

Cilleruelo, Javier; Kumchev, Angel; Luca, Florian; et al.;

Abstract:

We give various results about the distribution of the sequence {a(n)/n}(n >= 1) modulo 1, where a >= 2 is a fixed integer. In particular, we find an explicit infinite subsequence A such that {a(n)/n}(n is an element of A) is uniformly distributed modulo 1. Also we show that for any constant c > 0 and a sufficiently large N, the fractional parts of the first N terms of this sequence hit every interval subset of [0, 1] of length vertical bar vertical bar >= c N-0.475.