When 13 = 14

Why does Matthew say there “14 generations” between the Captivity and Christ, when anyone can count and see that he mentions 13 and not 14?

Specifically… Mat 1:17 So all the generations from Abraham to David were 14 generations; and from David until the exile to Babylon, 14 generations; and from the exile to Babylon until the Messiah, 14 generations.

So let’s count:

1 Abraham fathered
2 Isaac, Isaac fathered
3 Jacob, Jacob fathered
4 Judah and his brothers, Judah fathered
5 Perez and Zerah by Tamar, Perez fathered
6 Hezron, Hezron fathered
7 Aram, Aram fathered
8 Aminadab, Aminadab fathered
9 Nahshon, Nahshon fathered
10 Salmon, Salmon fathered
11 Boaz by Rahab, Boaz fathered
12 Obed by Ruth, Obed fathered
13 Jesse, and Jesse fathered
14 King David. Then David fathered
1 Solomon by Uriah’s wife, Solomon fathered
2 Rehoboam, Rehoboam fathered
3 Abijah, Abijah fathered
4 Asa, Asa fathered
5 Jehoshaphat, Jehoshaphat fathered
6 Joram, Joram fathered
7 Uzziah, Uzziah fathered
8 Jotham, Jotham fathered
9 Ahaz, Ahaz fathered
10 Hezekiah, Hezekiah fathered
11 Manasseh, Manasseh fathered
12 Amon, Amon fathered
13 Josiah, and Josiah fathered
14 Jechoniah and his brothers at the time of the exile to Babylon. Then after the exile to Babylon Jechoniah fathered

1 Salathiel, Salathiel fathered
2 Zerubbabel, Zerubbabel fathered
3 Abiud, Abiud fathered
4 Eliakim, Eliakim fathered
5 Azor, Azor fathered
6 Zadok, Zadok fathered
7 Achim, Achim fathered
8 Eliud, Eliud fathered
9 Eleazar, Eleazar fathered
10 Matthan, Matthan fathered
11 Jacob, and Jacob fathered
12 Joseph the husband of Mary, who gave birth to
13 Jesus who is called the Messiah.
(Mat 1:2-16 HCSB)

Uhhhhhhh…. am I missing someone? And you get the same numbers regardless of the version of Bible that you’re using. The only way I figure it is if you count “captivity” as a generation, then from “captivity” to the Messiah, you have 14 generations. But it doesn’t make sense to count “captivity” as a generation. ..does it?

Any ideas on this?

(We already talked about the time crunch where Abe -> David = ~1,000 years vs David -> captivity = ~500 years and captivity -> messiah = ~500 years. If you look at the specific timing for these folks, it looks like there are names missing between Perez and Salmon, or some verrrry old fathers (older than the ages of the other fathers mentioned during the time). I say this because this is a span of time that took at minimum 470 years, yet only 6 names are mentioned for that whole time (#5-#10), and Salmon was less than 60 years old when he married Rahab the Harlot, leaving 530 years for #1-#4 and #11-14. ..but I digress.)