What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …

Next two numbers are 15 and 32 respectively.

Step-by-step explanation:

The given pattern is  

45, 15, 44, 17, 40, 20, 31, 25, …

Here, we have two patterns.

Odd places : 45, 44, 40, 31,...

Even places : 15, 17, 20, 25,...

In series of odd places, we need to subtract square of integers.

So, 9th term of given pattern is  

In series of even places, we need to add prime numbers.

So, 10th term of given pattern is  

Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.