1,1

A073591(n) is an upper bound on a(n).

If the nodes of a complete graph with at least as many nodes as a(n) is colored with n colors then there is always a monochromatic triangle.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. Berman and K. D. Fryer, Introduction to Combinatorics. Academic Press, NY, 1972, p. 175.

H. W. Gould, personal communication.

R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math., 7 (1955), 1-7.

a(2)=6 since in a party with at least 6 people, there are three people mutually acquainted or three people mutually unacquainted.

Cf. A045652.

Sequence in context: A143093 A117712 A106158 this_sequence A073591 A078318 A074370

Adjacent sequences: A003320 A003321 A003322 this_sequence A003324 A003325 A003326

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Upper bound and additional comments from D. G. Rogers (drogers(AT)turing.une.edu.au), Aug 27 2006

Better definition from Max Alekseyev, Jan 12 2008