It has been conjectured that the sequence @math modulo @math is uniformly distributed. The distribution of this sequence is signifcant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we describe an algorithm to compute @math modulo @math to @math . We then statistically analyze its distribution. Our results strongly agree with the hypothesis that @math modulo 1 is uniformly distributed.
Let α be an arbitrary positive number. For every integer n ≦ 0 we can write where is the largest integer not greater than , i.e the integral part of , and r n is its fractional part and so satisfies the inequality