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%I #23 Apr 08 2022 05:56:19
%S 0,1,2,4,7,13,24,44,84,161
%N Least k such that there is a set S in {1, 2, ..., k} with n elements and the property that each of its subsets has a distinct sum.
%C The Conway-Guy sequence A005318 is an upper bound. Lunnon showed that a(67) < 34808838084768972989 = A005318(67), and Bohman improved the bound to a(67) <= 34808712605260918463.
%C Lunnon found a(0)-a(8) and J. P. Grossman found a(9).
%C a(10) > 220, with A201052. - _Fausto A. C. Cariboni_, Apr 06 2021
%H Tom Bohman, <a href="http://dx.doi.org/10.1090/S0002-9939-96-03653-2">A sum packing problem of Erdős and the Conway-Guy sequence</a>, Proc. AMS 124:12 (1996), pp. 3627-3636.
%H W. F. Lunnon, <a href="http://dx.doi.org/10.1090/S0025-5718-1988-0917837-5">Integer sets with distinct subset-sums</a>, Math. Comp. 50 (1988), pp. 297-320.
%e a(0) = 0: {}
%e a(1) = 1: {1}
%e a(2) = 2: {1, 2}
%e a(3) = 4: {1, 2, 4}
%e a(4) = 7: {3, 5, 6, 7}
%e a(5) = 13: {3, 6, 11, 12, 13}
%e a(6) = 24: {11, 17, 20, 22, 23, 24}
%e a(7) = 44: {20, 31, 37, 40, 42, 43, 44}
%e a(8) = 84: {40, 60, 71, 77, 80, 82, 83, 84}
%e a(9) = 161: {77, 117, 137, 148, 154, 157, 159, 160, 161}
%Y Cf. A005318, A201052.
%K nonn,hard,more,nice
%O 0,3
%A _Charles R Greathouse IV_ and J. P. Grossman, Sep 11 2016
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