Which number should come next and why: 2, 5, 12, 25, 54, 113, 240, 481, ?

Question

Find the number that comes next in the following series:

3, 7, 12, 14, 16, 19, 21, 25, 30, 41, 45, 52, 54, 56, 59, 61, 65, 70, ?

Answer 1

List of primes = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 ...
2 + (2nd prime which is just greater than 2)3 = 5
5 + (4th prime which is just greater than 5)7 = 12
12 + (6th prime which is just greater than 12)13 = 25
25 + (10th prime which is just greater than 25)29 = 54
54 + (17th prime which is just greater than 54)59 =113
113 + (31st prime which is just greater than 113)127 = 240
240 + (53rd prime which is just greater than 240)241 = 481
481 + (94th prime which is just greater than 481)487 = 968.