Irregularities in the distributions of finite sequences
Abstract
Suppose (x1, x2,..., xs+d) is a sequence of numbers with xi [set membership, variant] [0,1) which has the property that for each r <= s and for each k < r, the subinterval [k/r, (k + 1/n)) contains at least one point of the subsequence (x1, x2,..., xr+d). For fixed d, we wish to find the maximum s = s(d) for which such a sequence exists. We show that s(d) < 4(d+2)2 for all d and that s(0) = 17.
 Publication:

Journal of Number Theory
 Pub Date:
 May 1970
 DOI:
 10.1016/0022314X(70)900156
 Bibcode:
 1970JNT.....2..152B