Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.3

A Note on the Postage Stamp Problem


Amitabha Tripathi
Department of Mathematics
Indian Institute of Technology
Hauz Khas
New Delhi - 110016
India

Abstract: Let $h,k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $hA:=\{a_1+a_2+\cdots+a_r:a_i \in A, r \le h\}$ denote the set of all integers representable as a sum of no more than $h$ elements of $A$, and let $n(h,A)$ denote the largest integer $n$ such that $\{1,2,\ldots,n\} \subseteq hA$. Let $n(h,k)=\max_A\:n(h,A)$, where the maximum is taken over all sets $A$ with $k$ elements. The purpose of this note is to determine $n(h,A)$ when the elements of $A$ are in arithmetic progression. In particular, we determine the value of $n(h,2)$.

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(Concerned with sequences A014616 .)

Received July 1 2005; revised version received December 15 2005. Published in Journal of Integer Sequences December 15 2005.

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