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.