a(2) = 1667 because it is the first prime > 5 which is a palindrome in both base 3 and 5.
MATHEMATICA
Do[ k = n + 3; While[ a = IntegerDigits[ k, n ]; b = IntegerDigits[ k, n + 2 ]; !PrimeQ[ k ] || a != Reverse[ a ] || b != Reverse[ b ], k++ ]; Print[ k ], {n, 2, 10} ]
