That is part of the famous Fibonacci series, in which each number is the sum of the two number preceding it. This series shows up in various places in math and in the world of living things. The next two numbers are 21 and 34.
However, it would be equally true to say that the next two numbers are 11 and 12.
If you use the rule Un = (-n4 + 14n3 - 59n2 + 118n - 48)/24 for n = 1, 2, 3, ...
then U7 = 11 and U8 = 12
The pattern is plus 7. So the next number used to be 1.
21
58
If the last number is 1/3 (it should be), the next number is 5 and 1/3
21. Add the last 2 numbers to get the next.
The next number in the sequence is 18. It's +1, +2, +3, +4, ....
18
The pattern is plus 7. So the next number used to be 1.
21
58
If the last number is 1/3 (it should be), the next number is 5 and 1/3
23
21. Add the last 2 numbers to get the next.
34. Each number is the sum of the two preceding numbers. This is called the Fibonacci Sequence.
42 is the next number in this sequence. This number sequence is adding the next prime number to the last number. So 1 + 2 = 3. Then 3 + 3 = 6, 6 + 5 = 11, 11 + 7 = 18, 18 + 11 = 29. The next prime number after 11 is 13, so 29 + 13 = 42. The next numbers would be 59 (42+17), 78 (59+19), and 101 (78+23)
21. This is the Fibonacci series.
13, because if you add the last number to the current number you get the next number