Record values in appending and prepending bitstrings to runs of binary digits

Abstract

In this short note, we show a simple characterization of integers that reach records for a sequence described by adding binary strings to runs of 1's and 0's in a binary representation. In particular, we show that this set does not depend on the added strings as long as they are nonempty and of the same length.

4 pages, minor edits and corrected typos