11235813. What is the next number in this sequence?

The answer is 21.

Your numerical series is the beginning of a mathematical sequence called Fibonacci Numbers.

The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself (i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.).