OFFSET
0,3
COMMENTS
This sequence is the main entry for the distinct subset sums problem. See also A201052, A005318, A005255.
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.
Lunnon found a(0)-a(8) and J. P. Grossman found a(9).
a(10) > 220, with A201052. - Fausto A. C. Cariboni, Apr 06 2021
REFERENCES
Iskander Aliev, Siegel’s lemma and sum-distinct sets, Discrete Comput. Geom. 39 (2008), 59-66.
J. H. Conway and R. K. Guy, Solution of a problem of Erdos, Colloq. Math. 20 (1969), p. 307.
Dubroff, Q., Fox, J., & Xu, M. W. (2021). A note on the Erdos distinct subset sums problem. SIAM Journal on Discrete Mathematics, 35(1), 322-324.
R. K. Guy, Unsolved Problems in Number Theory, Section C8.
Marcin Mucha, Jesper Nederlof, Jakub Pawlewicz, Karol Węgrzycki, Equal-Subset-Sum Faster Than the Meet-in-the-Middle, arXiv:1905.02424
Stefan Steinerberger, Some remarks on the Erdős Distinct subset sums problem, International Journal of Number Theory, 2023 , #19:08, 1783-1800 (arXiv:2208.12182).
LINKS
Tom Bohman, A sum packing problem of Erdős and the Conway-Guy sequence, Proc. AMS 124:12 (1996), pp. 3627-3636.
J. H. Conway & R. K. Guy, Sets of natural numbers with distinct sums, Manuscript.
R. K. Guy, Letter to N. J. A. Sloane, Apr 1975
R. K. Guy, Sets of integers whose subsets have distinct sums, pp. 141-154 of Theory and practice of combinatorics. Ed. A. Rosa, G. Sabidussi and J. Turgeon. Annals of Discrete Mathematics, 12. North-Holland 1982.
R. K. Guy, Sets of integers whose subsets have distinct sums, pp. 141-154 of Theory and practice of combinatorics. Ed. A. Rosa, G. Sabidussi and J. Turgeon. Annals of Discrete Mathematics, 12. North-Holland 1982. (Annotated scanned copy)
W. F. Lunnon, Integer sets with distinct subset-sums, Math. Comp. 50 (1988), pp. 297-320.
EXAMPLE
a(0) = 0: {}
a(1) = 1: {1}
a(2) = 2: {1, 2}
a(3) = 4: {1, 2, 4}
a(4) = 7: {3, 5, 6, 7}
a(5) = 13: {3, 6, 11, 12, 13}
a(6) = 24: {11, 17, 20, 22, 23, 24}
a(7) = 44: {20, 31, 37, 40, 42, 43, 44}
a(8) = 84: {40, 60, 71, 77, 80, 82, 83, 84}
a(9) = 161: {77, 117, 137, 148, 154, 157, 159, 160, 161}
CROSSREFS
KEYWORD
nonn,hard,more,nice
AUTHOR
Charles R Greathouse IV and J. P. Grossman, Sep 11 2016
STATUS
approved