|Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.2|
Abstract: Consider the sequence of positive integers defined by and . Graham and Pollak discovered the unexpected fact that is just the -th digit in the binary expansion of . Fix . In this note, we first give two infinite families of similar nonlinear recurrences such that indicates the -th binary digit of . Moreover, for all integral , we establish a recurrence such that denotes the -th digit of in the -ary digital expansion.
(Concerned with sequences A001521 A091522 and A091523 .)
Received April 1 2005; revised version received May 12 2005. Published in Journal of Integer Sequences May 24 2005.