OFFSET
1,1
COMMENTS
Dombi's conjecture, now refuted, stated that there is no infinite set A such that the power series (sum(X^a, a>=0 not in A))^3 has strictly increasing coefficients. This sequence is conjecturally the lexicographically least such example---"conjecturally" because it is obtained by backtracking and there is currently no proof it can be extended to infinity.
LINKS
J. P. Bell and J. Shallit, Counterexamples to a conjecture of Dombi in additive number theory, Arxiv preprint arXiv:2212.12473 [math.NT], December 28 2022.
J. P. Bell and J. Shallit, Counterexamples to a conjecture of Dombi in additive number theory, Acta Math. Hung. (2023).
G. Dombi, Additive properties of certain sets, Acta Arith. 103 (2002), 137-146.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Apr 06 2023
STATUS
approved