Uncanny Subsequence Selections That Generate Normal Numbers

Given a real number 0_.a1a2a3 . . . that is normal to base b, we examine increasing sequences n_i so that the number 0_.an1an2an3 . . . are normal to base b. Classically, it is known that if the n_i form an arithmetic progression, then this will work. We give several more constructions including n_i that are recursively defined based on the digits a_i. Of particular interest, we show that if a number is normal to base b, then removing all the digits from its expansion which equal (b−1) leaves a base-(b−1) expansion that is normal to base (b − 1)