A288583 Related to study of weak Sidon sets.

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

Offset

1,2

Comments

From Bernd Mulansky, Jun 23 2021: (Start)

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).

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

(End)

References

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

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

Links

Table of n, a(n) for n=1..9.

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], 2017. See Problem C.65 p. 166.

Example

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.

Crossrefs

Cf. A004135.

Sequence in context: A146385 A039827 A004135 * A090036 A024971 A038084

Adjacent sequences: A288580 A288581 A288582 * A288584 A288585 A288586

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 06 2017

Status

approved