On a recursively defined sequence involving the prime counting function

Abstract

We prove some properties of sequence A335294 from the On-Line Encyclopedia of Integer Sequences, defined by an = ?(n) - ?(?n-1 k=1ak), where ?(x) is the number of primes ? x. In particular we show that the sequence (an) assumes every non-negative integral value infinitely often. © 2021, University of Waterloo. All rights reserved.