A359263 -id:A359263 - cp's OEIS frontend

A359264 First differences of A359263.

2, 3, 1, 2, 3, 4, 2, 3, 9, 6, 6, 4, 8, 6, 10, 11, 9, 12, 15, 12, 7, 20, 15, 13, 17, 15, 19, 20, 18, 19, 26, 21, 16, 29, 24, 27, 30, 27, 22, 35, 30, 25, 38, 33, 34, 35, 36, 34, 38, 36, 40, 41, 39, 40, 47, 42, 37, 50, 45, 46, 53, 48, 43, 56, 51, 46, 59, 54, 55

Offset: 0

Jeffrey Shallit, Dec 23 2022

nonn

Values of this sequence are positive, thus refuting a 2002 conjecture of Dombi discussed more fully in A359263.

Jeffrey Shallit, Counterexample to a Conjecture of Dombi in Additive Number Theory, arXiv:2212.12473 [math.NT], 2022.

Cf. A359263.

A362032 Lexicographically least counterexample to Dombi's conjecture.

Original entry on oeis.org

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

Jeffrey Shallit, Apr 06 2023

nonn

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.

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.

Cf. A359263, A359264.

cp's OEIS Frontend

A359264 First differences of A359263.

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