A001209 a(n) is the solution to the postage stamp problem with 4 denominations and n stamps. (Formerly M3432 N1568)

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

1,1

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.

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).

Sequence in context: A057305 A301211 A008195 * A227587 A128624 A372435

Adjacent sequences: A001206 A001207 A001208 * A001210 A001211 A001212

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved