**Question: **What are the next three numbers in the given series?

0 1 1 2 1 2 1 3 2 2 1 3 1 2 2 4 1 3 1 3 2 2 1 ? ? ?

**Answer:**

The next three numbers are 4, 2 and 2

The pattern is - the number of factors in prime factorization of positive integers. Note that all prime number positions are 1 in the given series.

Number Prime Factorization Factors in Prime Factorization

1 1 0

2 2 1

3 3 1

4 2*2 2

5 5 1

6 2*3 2

7 7 1

8 2*2*2 3

9 3*3 2

10 2*5 2

Thus, the next few numbers in the given series are:

4 2 2 3 3 1 3 1 5 2 2 2 4 1 2 2 4 1 3 1 3 3 2 1 5 2 3 2 3 1 4 2 4 2 2 1 ...

Note that 1 is neither a Prime number nor a Composite number.