A 76 INTEGERS 16 ( 2016 ) DISCRIMINATORS AND k - REGULAR SEQUENCES

The discriminator of an integer sequence s = (s(i))i 0, introduced by Arnold, Benkoski, and McCabe in 1985, is the map Ds(n) that sends n 1 to the least positive integer m such that the n numbers s(0), s(1), . . . , s(n 1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of two such sequences, the so-called “evil” and “odious” numbers, and show they are 2-regular. We give an example of a k-regular sequence whose discriminator is not k-regular. Finally, we examine sequences that are their own discriminators, and count the number of length-n finite sequences with this property.