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%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
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