(2(2n+1)+1)/3

Example:
211+1 = 2049
Representing this number in binary:
1 0 0 0 0 0 0 0 0 0 0 1
Regrouping for base 4: 211+1 = 2000014
10|00|00|00|00|01
Applying the sum of the digits proof:

10
00
00
00
00
01

11

As on can see adding 2 to the exponent will add 00 to the digits in the center of the base 4 representation. Therefore, since the digits add up to the base minus one, three; and no matter how many pairs of zeros we add to the expression the sum of the digits will remain three and therefore the original number is divisible by three.