## Postage Stamp Problem

Consider a Set of Integer denomination postage stamps with . Suppose they are to be used on an envelope with room for no more than stamps. The postage stamp problem then consists of determining the smallest Integer which cannot be represented by a linear combination with and . Exact solutions exist for arbitrary for and 3. The solution is

for . The general problem consists of finding

It is known that

(Stöhr 1955, Guy 1994), where is the Floor Function, the first few values of which are 2, 4, 7, 10, 14, 18, 23, 28, 34, 40, ... (Sloane's A014616).

References

Guy, R. K. The Postage Stamp Problem.'' §C12 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 123-127, 1994.

Sloane, N. J. A. Sequence A014616 in The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

Stöhr, A. Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe I, II.'' J. reine angew. Math. 194, 111-140, 1955.