A227358 Length of shortest Golomb-like (for sums of triples) ruler with n marks.

0, 1, 4, 11, 23, 45, 82, 129, 208, 309

Offset: 1

Author

John Tromp, Jul 08 2013

Keywords

• nonn
• hard
• more

Comments

a(n) is the least integer such that there is an n-element set of integers between 0 and a(n), the sums of triples (of not necessarily distinct elements) of which are distinct.

a(11) = 445 or a(11) < 440, but disproving the latter will take many cpu-years with the given program. - John Tromp, Aug 28 2013

Examples

			a(4) = 11 because 0-1-7-11 (0-4-10-11) and 0-1-8-11 (0-3-10-11) have all (6 choose 3)=20 distinct triple sums and there is no 0=b0<b1<b2<b3<11 with distinct triple sums.
		

Links

• IBM Research, Ponder This, July 2013 essentially asks for a(8).
• Kevin O'Bryant, Constructing Thick B_h sets, arXiv:2308.12406 [math.NT], 2023.
• John Tromp, PonderThisJuly2013.c

Crossrefs

Cf. A003022, A227588.

Programs

C

// See link.

Formula

a(n) = A227588(n,3) - 1. - James Wilcox, Aug 02 2013

Extensions

a(8)-a(10) from John Tromp, Jul 30 2013