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 and infinite subsequence A such that {a n /n} n∈A is well distributed.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 J ⊆ [0, 1] of length |J | ≥ cN -0.475 .