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Related to study of weak Sidon sets.
1

%I #19 Jul 27 2021 12:29:13

%S 1,2,3,6,11,19,28,42,56

%N Related to study of weak Sidon sets.

%C From _Bernd Mulansky_, Jun 23 2021: (Start)

%C Additive bases: a(n) is the least integer k such that in each cyclic group Z_j with j>=k there is a subset of n elements all pairs (of distinct elements) of which add up to a different sum (in Z_j).

%C Such subsets are known as (modular) weak Sidon sets, weak B_2 sets, or well-spread sequences.

%C (End)

%D Bela Bajnok, Additive Combinatorics: A Menu of Research Problems. Chapman & Hall/CRC, 2018. See Problem C.65.

%D A. Maturo and D. Yager-Elorriaga, Finding Sidon sets in abelian groups. Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 7 (2008).

%H Bela Bajnok, <a href="https://arxiv.org/abs/1705.07444">Additive Combinatorics: A Menu of Research Problems</a>, arXiv:1705.07444 [math.NT], 2017. See Problem C.65 p. 166.

%e Z_j contains a weak Sidon set of size 8 for j=40 and for every j>=42, but not for j=41, hence a(8)=42.

%Y Cf. A004135.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Jul 06 2017