Van der Corput sequence

A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base-n representation of the sequence of natural numbers (1, 2, 3, …). A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base-n representation of the sequence of natural numbers (1, 2, 3, …). The b-ary representation of the positive integer n (≥ 1) is where b is the base in which the number n is represented, and 0 ≤ dk(n) < b, i.e. the k-th digit in the b-ary expansion of n.The n-th number in the van der Corput sequence is For example, to get the decimal van der Corput sequence, we start by dividing the numbers 1 to 9 in tenths (x/10), then we change the denominator to 100 to begin dividing in hundredths (x/100). In terms of numerator, we begin with all two-digit numbers from 10 to 99, but in backwards order of digits. Consequently, we will get the numerators grouped by the end digit. Firstly, all two-digit numerators that end with 1, so the next numerators are 01, 11, 21, 31, 41, 51, 61, 71, 81, 91. Then the numerators ending with 2, so they are 02, 12, 22, 32, 42, 52, 62, 72, 82, 92. An after the numerators ending in 3: 03, 13, 23 and so on...