We give a number of results about families of Ulam sequences and sets, further exploring recent work on rigidity phenomena. For Ulam sequences, using elementary methods we give an upper bound on the density and prove regularity for various families of sequences. For Ulam sets, we consider extensions of classification work done by Kravitz and Steinerberger.
"Rigidity of Ulam sets and sequences." Involve 12 (3) 521 - 539, 2019. https://doi.org/10.2140/involve.2019.12.521