On a Conjecture about Ron Graham's Sequence

2024/10/07 by Peter Kagey, Kagey, Peter, Krishna Rajesh +1 · 1 voice · 1 citation
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.2410.04728

arxiv published 2024/10/07 · arxiv updated 2024/10/11

Abstract

Ron Graham's Sequence is a surprising bijection from non-negative integers to non-negative, non-prime integers that was introduced by Ron Graham in the June 1986 "Problems" column of Mathematics Magazine, and which later appeared in Problem A2 of the 2013 William Lowell Putnam Mathematical Competition. We describe some properties of this function, give an algorithm for computing its values in pseudo-polynomial time, and prove a 22 year-old conjecture about an upper bound for the function.

Cited by

• On a Generalisation of a Function of Ron Graham's

Discussions

• My first sequence, which I learned about from taking the Putnam, is based on a very cool idea from Ron Graham and is usually called "Ron Graham's Sequence." I've since supervised a senior thesis stude [bsky, 1 points, 1 comments]

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