The Challenge: It is time to put your problem solving skills to test.

1, 1, 1, 4, 7, 6, 20, 8, 9, 10, _, _, _, _, _

Simply write down the postions of each numbers below it:

1, 1, 1, 4, 7, 6, 20, 8, 9, 10, _, _, _, _, _ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

We see that each prime position is replaced.

Careful analysis shows that each prime position is replaced by sum of the numbers before the position.

So the next number at 11 will change as 11 is prime and it will be 1 + 1 + 1 + 4 + 7 + 6 + 20 + 8 + 9 + 10 = 67

12, 14 and 15 will remain unchanged but 13 likewise changes to 146.

So the completed sequence will be 1, 1, 1, 4, 7, 6, 20, 8, 9, 10, 67, 12, 146, 14, 15