4, 7, 25, 10, __, 20, 16, 19. What number should fill the blank?

The answer is 13.

The sequence is a list of numbers, each of which is the sum of the two numbers that come before it. So, the first number is 4, and the second number is 7, which is the sum of 4 and 3. The third number is 25, which is the sum of 7 and 18. The fourth number is 10, which is the sum of 25 and 5. The fifth number is 13, which is the sum of 10 and 3. The sixth number is 20, which is the sum of 13 and 7. The seventh number is 16, which is the sum of 20 and 6. The eighth number is 19, which is the sum of 16 and 3.

Therefore, the number that should fill the blank is 13.