A362032 Lexicographically least counterexample to Dombi's conjecture.

3, 6, 9, 12, 16, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 44, 50, 56, 60, 61, 62, 63, 69, 70, 71, 72, 74, 82, 88, 89, 90, 91, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 122, 125, 129, 130, 131, 133, 134, 136, 140, 143, 147, 148, 149

Offset: 1

Author

Jeffrey Shallit, Apr 06 2023

Keywords

• nonn

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

Cf. A359263, A359264.