

A001212


a(n) = solution to the postage stamp problem with n denominations and 2 stamps.
(Formerly M1089 N0972)


27



2, 4, 8, 12, 16, 20, 26, 32, 40, 46, 54, 64, 72, 80, 92, 104, 116, 128, 140, 152, 164, 180, 196, 212
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OFFSET

1,1


COMMENTS

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.
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


REFERENCES

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. K. Guy, Unsolved Problems in Number Theory, C12.
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).


LINKS

Table of n, a(n) for n=1..24.
R. Alter, Letter to N. J. A. Sloane, Mar 25 1977
R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206210.
M. F. Challis, Two new techniques for computing extremal hbases A_k, Comp J 36(2) (1993) 117126
M. F. Challis and J. P. Robinson, Some Extremal Postage Stamp Bases, J. Integer Seq., 13 (2010), Article 10.2.3.
Erich Friedman, Postage stamp problem
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382404.
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs
F. H. Kierstead, Jr.,, The Stamp Problem, J. Rec. Math., Vol. ?, Year ?, page 298. [Annotated and scanned copy]
J. Kohonen, A meetinthemiddle algorithm for finding extremal restricted additive 2bases, arXiv preprint arXiv:1403.5945, 2014 and J. Int. Seq. 17 (2014) # 14.6.8.
J. Kohonen, J. Corander, Addition Chains Meet Postage Stamps: Reducing the Number of Multiplications, J. Integer Seq., 17 (2014), Article 14.3.4.
J. Kohonen, Early Pruning in the Restricted Postage Stamp Problem, arXiv preprint arXiv:1503.03416, 2015
W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377380.
W. F. Lunnon, A postage stamp problem [Annotated scanned copy]
J. P. Robinson, Some postage stamp 2bases, JIS 12 (2009) 09.1.1.
E. S. Selmer, Letter to N. J. A. Sloane, Sep 10 1991
Eric Weisstein's World of Mathematics, Postage stamp problem
Mingjia Yang, An experimental walk in patterns, partitions, and words, Ph. D. Dissertation, Rutgers University (2020).


CROSSREFS

Postage stamp sequences: A001208 A001209 A001210 A001211 A001212 A001213 A001214 A001215 A001216 A005342 A005343 A005344 A014616 A053346 A053348 A075060 A084192 A084193
Cf. A006638, A123509.
Equals A196094(n)  1 and A234941(n+1)2.
A row or column of the array A196416 (possibly with 1 subtracted from it).
Sequence in context: A221707 A186146 A006638 * A160742 A160736 A118030
Adjacent sequences: A001209 A001210 A001211 * A001213 A001214 A001215


KEYWORD

nonn,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

Corrected a(17). Added a(18) and a(19) from Challis.  R. J. Mathar, 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 (johnrobinson(AT)uiowa.edu), Feb 19 2010
Added term a(23) from Challis and Robinson's July 2013 addendum, by Jukka Kohonen, Oct 25 2013
Added a(24) from Kohonen and Corander (2013).  N. J. A. Sloane, Jan 08 2014


STATUS

approved



