A118771 Let a "sum" be a set {x,y,z} of distinct natural numbers such that x+y=z and let N_m={1,2,...m}. a(n) is the smallest s such that there is no partition of N_s into n sum-free parts.

3, 9, 24, 67

Offset: 1

Author

R. Reis (rvr(AT)ncc.up.pt), May 22 2006

Keywords

• nonn
• hard
• more

Comments

a(5) >= 190 (see Blanchard et al. at p. 7). - Michel Marcus, Mar 26 2013

a(5) >= 197, a(6) >= 583, a(7) >= 1741, a(8) >= 5202, a(9) >= 15597 (see Ahmed et al. at p. 3). - Stefano Spezia, Aug 25 2023

Examples

			For n=1, a(1)=3 as there is no partition of N_3={1,2,3} into 1-sum-free parts. In the same way a(2)=9...
		

Links

• T. Ahmed, L. Boza, M. P. Revuelta, and M. I. Sanz, Exact values and lower bounds on the n-color weak Schur numbers for n=2,3. Ramanujan J (2023). See Table 2 at p. 3.
• P. Blanchard, F. Harary, and R. Reis, Partitions into sum-free sets, Integers: electronic journal of combinatorial number theory, 6. 2006.

Crossrefs

Cf. A030126, A072842.