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A001212
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a(n) = solution to the postage stamp problem with n denominations and 2 stamps.
(Formerly M1089 N0972)
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25
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2, 4, 8, 12, 16, 20, 26, 32, 40, 46, 54, 64, 72, 80, 92, 104, 116, 128, 140, 152, 164, 180
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
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
The g.f. 2*(1+2*z**2+2*z+3*z**3+3*z**4+2*z**6)/(z-1)/(3*z**5-z**4+z**2-z-1) conjectured by S. Plouffe in his 1992 dissertation is wrong.
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REFERENCES
| R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, p. 115 (Coins of the Realm), 1984.
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382-404.
R. K. Guy, Unsolved Problems in Number Theory, C12.
W. F. Lunnon, A postage stamp problem. Comput. J. 12 (1969) 377-380.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| M. F. Challis, Twonew techniques for computing extremal h-bases A_kComp J 36(2) (1993) 117-126
M. F. Challis and J. P. Robinson, Some Extremal Postage Stamp Bases, J. Integer Seq., 13 (2010), Article 10.2.3. [From John P Robinson (john-robinson(AT)uiowa.edu), Feb 19 2010]
Erich Friedman, Postage stamp problem
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Postage stamp problem
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CROSSREFS
| Postage stamp sequences: A001208 A001209 A001210 A001211 A001212 A001213 A001214 A001215 A001216 A005342 A005343 A005344 A014616 A053346 A053348 A075060 A084192 A084193
Cf. A006638.
Equals A196094 - 1.
A row or column of the array A196416 (possibly with 1 subtracted from it).
Sequence in context: A160408 A186146 A006638 * A160742 A160736 A118030
Adjacent sequences: A001209 A001210 A001211 * A001213 A001214 A001215
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected a(17). Added a(18) and a(19) from Challis. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2006
Entry improved by comments from John Seldon (johnseldon(AT)onetel.com), Sep 15 2004
a(20) from Tim Peters (tim.one(AT)comcast.net), Oct 04 2006
Added terms a(21) and a(22) from Challis and Robinson. John P Robinson (john-robinson(AT)uiowa.edu), Feb 19 2010
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