A001209 a(n) is the solution to the postage stamp problem with 4 denominations and n stamps.

4, 12, 24, 44, 71, 114, 165, 234, 326, 427, 547, 708, 873, 1094, 1383, 1650, 1935, 2304, 2782, 3324, 3812, 4368, 5130, 5892, 6745, 7880, 8913, 9919, 11081, 12376, 13932, 15657, 17242, 18892, 21061, 23445, 25553, 27978, 31347, 33981, 36806, 39914, 43592

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Challis lists up to a(54) and provides recursions up to a(157). - R. J. Mathar, Apr 01 2006

Additional terms a(29) through a(254) can be computed using 3 sets of equations and a table of 10 coefficients available on line at Challis and Robinson. - John P Robinson (john-robinson(AT)uiowa.edu), Feb 18 2010

References

• 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

• Robert Price, Table of n, a(n) for n = 1..54
• R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
• M. F. Challis, Two new techniques for computing extremal h-bases A_k, Comp. 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.
• Erich Friedman, Postage stamp problem
• W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377-380.
• S. Mossige, Algorithms for Computing the h-Range of the Postage Stamp Problem, Math. Comp. 36 (1981) 575-582.
• Eric Weisstein's World of Mathematics, Postage stamp problem

Crossrefs

Postage stamp sequences: A001208, A001209, A001210, A001211, A001212, A001213, A001214, A001215, A001216, A005342, A005343, A005344, A014616, A053346, A053348, A075060, A084192, A084193.

Equals A196069 - 1.

A row or column of the array A196416 (possibly with 1 subtracted from it).

Extensions

Entry improved by comments from John Seldon (johnseldon(AT)onetel.com), Sep 15 2004

a(15) to a(28) from Table 1 of Mossige reference added by R. J. Mathar, Mar 29 2006

a(29)-a(54) from Challis and Robinson added by Robert Price, Jul 19 2013