The numbers are increasing by 1,4,9,16,25,36.... which are square numbers so the next increase is 49. Making the next number in the sequence 141
This list of numbers is the list of prime numbers. Following 11, the next two numbers in the list are 13 and 17.
15... you're dividing by 2 each time.
Two possible answers spring immediately to mind. First, this sequence appears to be a list of the first five prime numbers; in this case, the next number in the sequence would be 13. Second, the intervals between these numbers comprise the sequence "1 2 2 4", in which the nth number equals the product of the (n-1)th and (n-2)th numbers. Based on this, the next number in the given sequence would be 11 + (4*2) = 19.
The next number in the sequence would be 23. The sequence consists of prime numbers.
13, 21 - it is the Fibonacci sequence