Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.3 |

Islamic Azad University

Dolatabad Branch

Isfahan

Iran

Madjid Mirzavaziri

Department of Pure Mathematics

Ferdowsi University of Mashhad

P. O. Box 1159-91775

Iran

**Abstract:**

Let be a subset of
. We say that is -full if
for a positive integer , where is the set of
all positive integers which are a sum of distinct elements of and
. In this paper, we show that a set
with
is full if and only if
and
for each
.
We also prove that for each positive integer
there is an -full set. We determine the numbers
and
in terms of . We also give a formula for , the number of
-full sets.

(Concerned with sequences A188429 A188430 A188431.)

Received June 3 2010;
revised version received December 3 2010; April 20 2011.
Published in *Journal of Integer Sequences*,
April 22 2011.

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