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%I M1089 N0972 #102 Dec 19 2021 09:56:50
%S 2,4,8,12,16,20,26,32,40,46,54,64,72,80,92,104,116,128,140,152,164,
%T 180,196,212
%N a(n) = solution to the postage stamp problem with n denominations and 2 stamps.
%C _Fred Lunnon_ [W. F. Lunnon] defines "solution" to be the smallest value not obtainable by the best set of stamps. The solutions given are one lower than this, that is, the sequence gives the largest number obtainable without a break using the best set of stamps.
%C a(20)=152: There is only one set of 20 denominations covering all sums through 152: {1, 3, 4, 5, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 71, 72, 73, 75, 76}. - Tim Peters (tim.one(AT)comcast.net), Oct 04 2006
%D Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, p. 115 (Coins of the Realm), 1984.
%D R. K. Guy, Unsolved Problems in Number Theory, C12.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. Alter, <a href="/A001212/a001212.pdf">Letter to N. J. A. Sloane, Mar 25 1977</a>
%H R. Alter and J. A. Barnett, <a href="http://www.jstor.org/stable/2321610">A postage stamp problem</a>, Amer. Math. Monthly, 87 (1980), 206-210.
%H M. F. Challis, <a href="http://dx.doi.org/10.1093/comjnl/36.2.117">Two new techniques for computing extremal h-bases A_k</a>, Comp J 36(2) (1993) 117-126
%H M. F. Challis and J. P. Robinson, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL13/Challis/challis6.html">Some Extremal Postage Stamp Bases</a>, J. Integer Seq., 13 (2010), Article 10.2.3.
%H Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0403.html">Postage stamp problem</a>
%H R. L. Graham and N. J. A. Sloane, <a href="http://dx.doi.org/10.1137/0601045">On Additive Bases and Harmonious Graphs</a>, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382-404.
%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>
%H F. H. Kierstead, Jr.,, <a href="/A001208/a001208.pdf">The Stamp Problem</a>, J. Rec. Math., Vol. ?, Year ?, page 298. [Annotated and scanned copy]
%H J. Kohonen, <a href="http://arxiv.org/abs/1403.5945">A meet-in-the-middle algorithm for finding extremal restricted additive 2-bases</a>, arXiv preprint arXiv:1403.5945, 2014 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Kohonen2/kohonen5.html">J. Int. Seq. 17 (2014) # 14.6.8</a>.
%H J. Kohonen, J. Corander, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL17/Kohonen/kohonen2.html">Addition Chains Meet Postage Stamps: Reducing the Number of Multiplications</a>, J. Integer Seq., 17 (2014), Article 14.3.4.
%H J. Kohonen, <a href="http://arxiv.org/abs/1503.03416">Early Pruning in the Restricted Postage Stamp Problem</a>, arXiv preprint arXiv:1503.03416, 2015
%H W. F. Lunnon, <a href="http://dx.doi.org/10.1093/comjnl/12.4.377">A postage stamp problem</a>, Comput. J. 12 (1969) 377-380.
%H W. F. Lunnon, <a href="/A001212/a001212_2.pdf">A postage stamp problem</a> [Annotated scanned copy]
%H J. P. Robinson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Robinson/robinson4.html">Some postage stamp 2-bases</a>, JIS 12 (2009) 09.1.1.
%H E. S. Selmer, <a href="/A001212/a001212_1.pdf">Letter to N. J. A. Sloane, Sep 10 1991</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PostageStampProblem.html">Postage stamp problem</a>
%H Mingjia Yang, <a href="https://doi.org/10.7282/t3-d9z1-aw94">An experimental walk in patterns, partitions, and words</a>, Ph. D. Dissertation, Rutgers University (2020).
%Y Postage stamp sequences: A001208 A001209 A001210 A001211 A001212 A001213 A001214 A001215 A001216 A005342 A005343 A005344 A014616 A053346 A053348 A075060 A084192 A084193
%Y Cf. A006638, A123509.
%Y Equals A196094(n) - 1 and A234941(n+1)-2.
%Y A row or column of the array A196416 (possibly with 1 subtracted from it).
%K nonn,nice,more
%O 1,1
%A _N. J. A. Sloane_
%E Corrected a(17). Added a(18) and a(19) from Challis. - _R. J. Mathar_, Apr 01 2006
%E Entry improved by comments from John Seldon (johnseldon(AT)onetel.com), Sep 15 2004
%E a(20) from Tim Peters (tim.one(AT)comcast.net), Oct 04 2006
%E Added terms a(21) and a(22) from Challis and Robinson. John P Robinson (john-robinson(AT)uiowa.edu), Feb 19 2010
%E Added term a(23) from Challis and Robinson's July 2013 addendum, by _Jukka Kohonen_, Oct 25 2013
%E Added a(24) from Kohonen and Corander (2013). - _N. J. A. Sloane_, Jan 08 2014
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