Fill in the blanks. All the sequences below follow the same pattern.

1.) 0

2.) 1, 1, 1, 1, 1, 1, 1, 1...

3.) 2, 2, 2, 2, 2, 2, 2, 2...

4.) 5, 5, 5, 5, 5, 5, 5, 5...

5.) 4, 8, 64, 2097152 ...

6.) 6, 36, 10077696 ...

7.) 7, 7, 7, 7, 7, 7, 7, 7...

8.) 9, 27, 729, 14348907 ...

9.) 10, 100, ____, ....

10.) 11, ____ ....

I think I know the answer to the sequence puzzle, but only if the last number listed for sequence no.8 is incorrect.

My answer is that the next number in the sequence is the product of all divisors (evenly) of the previous number. Sequences that start with prime numbers or 1, continue with the same value, since for example for 5, the product of the divisors is just 1 x 5 = 5, which continues forever.

Things do get interesting for sequences that start with composite numbers though. Like 4,8,64,... the next number is 1 x 2 x 4 x 8 x 16 x 32 x 64 = 2097152.

Similarly for 36: 1 x 2 x 3 x 4 x 6 x 9 x 12 x 18 x 36 = 10077696

Then for 9.) 10, 100, 1,000,000,000

and 10.) 11, 11

With this logic, no. 8 is much larger, approx. 1.046035 x 10 ^10.