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%I #44 Aug 29 2023 11:51:37
%S 0,1,4,11,23,45,82,129,208,309
%N Length of shortest Golomb-like (for sums of triples) ruler with n marks.
%C 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.
%C 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
%H IBM Research, <a href="http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/July2013.html">Ponder This, July 2013</a> essentially asks for a(8).
%H Kevin O'Bryant, <a href="https://arxiv.org/abs/2308.12406">Constructing Thick B_h sets</a>, arXiv:2308.12406 [math.NT], 2023.
%H John Tromp, <a href="/A227358/a227358.c.txt">PonderThisJuly2013.c</a>
%F a(n) = A227588(n,3) - 1. - _James Wilcox_, Aug 02 2013
%e 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.
%o See link.
%Y Cf. A003022, A227588.
%K nonn,hard,more
%O 1,3
%A _John Tromp_, Jul 08 2013
%E a(8)-a(10) from _John Tromp_, Jul 30 2013
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