Last digits indicates Prime numbers... and addition of first digits of 2 consecutive terms in the given series gives the first digit of next number..

In the given series;

02 --> 0 is the first digit and 2 is the last digit, 2 is a prime

13 --> 1 is the first digit and 3 is the last digit, 3 is a prime

Now, adding 0 + 1 = 1; next prime after 3 is '5'

so, 15 is the next digit.

Now, 1 + 1 = 2; next prime after 5 is '7',

Therefore, next number in the sequence is 27

Now, 2 + 1 = 3, next prime after 7 is 11'

Then, next number in the sequence is '311'

Now, 3 + 2 = 5; next prime after 11 is '13'

then, next number in the sequence is '513'

In the same way,

5 + 3 = 8; next prime after 13 is '17'

Then, The next number in the sequence become '817'