Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.4 |

School of Mathematical Sciences and Institute of Mathematics

Nanjing Normal University

Nanjing 210023

P. R. China

**Abstract:**

For a set *T* of integers, let *P*(*T*) be the set
of all finite subset sums of *T*, and let *T*(*x*) be the set of all
integers of *T* not exceeding *x*. Let
be a sequence of integers and *d*_{1}=10,
*d*_{2}=3*b*_{1}+4, and
*d*_{n}=3*b*_{n-1}+2 .
In this paper, we prove that

(i) if *b*_{n}>*d*_{n} for all ,
then there
exists a sequence of positive integers
such that, for all ,
;

(ii) if *b*_{m}=*d*_{m} for some
and
*b*_{n}>*d*_{n} for all ,
then there is no such sequence
*A*.

We also pose a problem for further research.

Received May 7 2013;
revised version received September 5 2013.
Published in *Journal of Integer Sequences*, October 12 2013.

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