Problem:
How many of the first ten numbers of the sequence 121,11211,1112111,β¦ are prime numbers?
Answer Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Solution:
Note that
121112111112111β=110+11=11β
(10+1),=11100+111=111β
(100+1),=1111000+1111=1111β
(1000+1),β
and so on. Therefore each number in the sequence can be written as a product of two positive integers, each greater than 1 , so none of the numbers in this sequence is prime.
The problems on this page are the property of the MAA's American Mathematics Competitions