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 A362032 Lexicographically least counterexample to Dombi's conjecture. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..59. 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. Sequence in context: A194199 A072567 A186353 * A061796 A113241 A310153 Adjacent sequences: A362029 A362030 A362031 * A362033 A362034 A362035 KEYWORD nonn AUTHOR Jeffrey Shallit, Apr 06 2023 STATUS approved

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Last modified September 16 07:48 EDT 2024. Contains 375959 sequences. (Running on oeis4.)