2007 AMC 12B Problem 21

The first 2007 positive integers are each written in base 3. How many of these base-3 representations are palindromes? (A palindrome is a number that reads the same forward and backward.)

\mathrm {(A)} 100\qquad \mathrm {(B)} 101\qquad \mathrm {(C)} 102\qquad \mathrm {(D)} 103\qquad \mathrm {(E)} 104

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.