**A**,

**B**and

**C**are polynomial increasing sequences of positive integers.

1.

**A(k) + B(k) = C(k)**

2.

**A(8)**is a square

3.

**C(8)**= 128.

Both

**A**and

**B**series have only one prime number as a member.

Each member of

**C**is evenly divisible by at least one square (other than 1) number.

How are the sequences

**A**,

**B**and

**C**defined?

What's so special about them?