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Search: id:A001208
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| A001208 |
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a(n) = solution to the postage stamp problem with 3 denominations and n stamps.
(Formerly M2721 N1351)
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+0
20
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| 3, 8, 15, 26, 35, 52, 69, 89, 112, 146, 172, 212, 259, 302, 354, 418, 476, 548, 633, 714, 805, 902, 1012, 1127, 1254, 1382, 1524, 1678, 1841, 2010, 2188, 2382, 2584, 2801, 3020, 3256, 3508, 3772, 4043, 4326, 4628, 4941, 5272, 5606, 5960, 6334, 6723, 7120
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
R. K. Guy, Unsolved Problems in Number Theory, C12.
W. F. Lunnon, A postage stamp problem. Comput. J. 12 (1969) 377-380.
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LINKS
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Erich Friedman, Postage stamp problem
Eric Weisstein's World of Mathematics, Postage stamp problem
M. F. Challis, Two new techniques for computing extremal h-bases A_kComp. J. 36(2) (1993) 117-126
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MAPLE
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c2 :=array(0..8, [3, 3, 5, 5, 7, 6, 8, 8, 10]) ; c3 :=array(0..8, 1..2, [[1, 1], [1, 1], [2, 1], [2, 1], [3, 1], [2, 2], [3, 2], [3, 2], [4, 2]]); c4 :=array(0..8, 1..3, [[0, 0, 0], [0, 0, 1], [1, 0, 1], [1, 0, 2], [2, 0, 2], [2, 1, 2], [3, 1, 2], [3, 1, 3], [4, 1, 3]]) ; for n from 23 to 100 do r := n mod 9 ; t := iquo(n, 9) ; a2 := 6*t+c2[r] ; a3 := (2*t+c3[r, 1])+(2*t+c3[r, 2])*a2 ; printf("%a, ", 4*t+c4[r, 1]+(2*t+c4[r, 2])*a2+(3*t+c4[r, 3])*a3) ; end: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2006
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CROSSREFS
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Postage stamp sequences: A001208 A001209 A001210 A001211 A001212 A001213 A001214 A001215 A001216 A005342 A005343 A005344 A014616 A053346 A053348 A075060 A084192 A084193
Sequence in context: A022451 A080181 A071399 this_sequence A159465 A071148 A048598
Adjacent sequences: A001205 A001206 A001207 this_sequence A001209 A001210 A001211
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Added Maple recursion program valid for n>=23 from Challis. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2006
At least 64 terms are known, see Friedman link.
Entry improved by comments from John Seldon (johnseldon(AT)onetel.com), Sep 15 2004
More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006
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