A072842

[Don Reble]

> %S A072842 2,8,23,52
> %N A072842 Largest m such that we can partition the set {1,2,...,m} into
>     n disjoint subsets with the property that we never have a+b=c for
>     any a, b, c in any of the subsets.
> %C A072842 The fourth number may be erroneous.
> %e A072842 max(m(2)) = 8 because we may partition the set into
>     {1, 3, 5, 8} and {2, 4, 6, 7} but in no other ways; attempting to
>     add 9 to either will produce a set with the property that a+b=c for
>     some a,b,c (1+8=9 or 2+7=9)
> %A A072842 Tor G. J. Myklebust (pi at flyingteapot.bnr.usu.edu), Jul 24 2002

    The example should be { 1 2 4 8 } { 3 5 6 7 }.

    a(4) is at least 58.
	{ 1 2 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 }
	{ 3 5 6 12 20 27 41 42 56 57 }
	{ 8 9 11 14 15 18 21 47 48 50 51 53 54 }
	{ 17 23 24 26 29 30 32 33 35 36 38 39 44 45 }
    Hmm... If it is exactly 58, my little program would need about 10^15
    years to prove it. Don't wait up.

--
Don Reble       djr at nk.ca