Results

**1 - 3**of**3**### A note on irregularities of distribution

, 2013

"... Let d ≥ 0 be a fixed integer. Suppose X = (x1, x2,..., xN) is a sequence in [0, 1) with the property that for every n ≤ N − d, each of the intervals [ k−1 k,), 1 ≤ k ≤ n, contains at least one xi with 1 ≤ i ≤ n + d. n n We show that N = O(d 3). This is a generalization of question raised by Steinhau ..."

Abstract
- Add to MetaCart

(Show Context)
Let d ≥ 0 be a fixed integer. Suppose X = (x1, x2,..., xN) is a sequence in [0, 1) with the property that for every n ≤ N − d, each of the intervals [ k−1 k,), 1 ≤ k ≤ n, contains at least one xi with 1 ≤ i ≤ n + d. n n We show that N = O(d 3). This is a generalization of question raised by Steinhaus some 50 years ago. 1 Introduction. In [4], H. Steinhaus [4] raised the following question. Does there exist for every positive integer N, a sequence of real numbers x1, x2,..., xN in [0, 1) such that every n ∈ {1, 2,..., N} and every k ∈ {1, 2,..., n}, we have

### #A53 INTEGERS 13 (2013) A NOTE ON IRREGULARITIES OF DISTRIBUTION

"... Let d ≥ 0 be a fixed integer. Suppose X = (x1, x2, x3,...) is a sequence in [0, 1) with the property that for every n ≤ N, each of the intervals [ k−1 k n ..."

Abstract
- Add to MetaCart

(Show Context)
Let d ≥ 0 be a fixed integer. Suppose X = (x1, x2, x3,...) is a sequence in [0, 1) with the property that for every n ≤ N, each of the intervals [ k−1 k n