Strange? Primes and Palindromes have no business being in this Place?

Question

$1$

$1$,$2$ Good easy start

$1$,$2$,$4$ As expected

$1$,$2$,$4$,$8$ I know it is going to be easy

$1$,$2$,$4$,$8$,$16$ why is he giving this? I got it!

$1$,$2$,$4$,$8$,$16$,Prime ...oops!..why is it here?

$1$,$2$,$4$,$8$,$16$,Prime, Odd...sure this is odd

$1$,$2$,$4$,$8$,$16$,Prime,Odd,Palindrome...this sure is strange and wierd?

Maybe, oeis will help me..oh no..

Looks like I have to put my thinking cap and get a solution for those 3 missing members.

Answer 1

Maybe, oeis will help me..oh no.. _{this puzzle is spoiled}

Answer is:

31 (prime), 57 (odd), 99 (palindrome)

Key to this is:

Maximal number of regions obtained by joining $n$ points around a circle by straight lines