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A004129 Postage stamp problem: largest m such that there exists an n-subset S of nonnegative integers such that 1,...,m can be expressed as a sum of two distinct elements of S.
(Formerly M2525)
0

%I M2525 #41 Apr 13 2022 13:25:17

%S 1,3,6,9,13,17,22,27,33,40,47,56,65,74,83,94,105

%N Postage stamp problem: largest m such that there exists an n-subset S of nonnegative integers such that 1,...,m can be expressed as a sum of two distinct elements of S.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. L. Graham and N. J. A. Sloane, <a href="http://neilsloane.com/doc/RLG/073.pdf">On Additive Bases and Harmonious Graphs</a>, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382-404, doi:10.1137/0601045.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Pos#postage_stamp_problem">Index to sequences related to the postage stamp problem</a>

%F The g.f. (z^4+z^3+2*z^2+2*z+1)*(z^2+z+1)/((z-1)*(z^5+z^4+z^3-z-1)) conjectured by _Simon Plouffe_ in his 1992 dissertation is wrong. - _Sean A. Irvine_, Nov 21 2015

%F At present no g.f. is known. - _N. J. A. Sloane_, Jan 14 2021

%K nonn,more

%O 2,2

%A _N. J. A. Sloane_

%E a(15)-a(18) from _Sean A. Irvine_, Nov 21 2015

%E Definition corrected by _Rob Pratt_, Jan 14 2021

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)