[Edit] Note to the reader, this post consists of material that I have posted elsewhere on the Internet. After nearly 20 years of doing this I have a great deal of material that I have used for the same sort of discussions. I guess that isn't fair and I will be editing and rewording all of the posts that I have made here using this method. I have an inactive forum which I use to store this stuff, but I have also posted much of it on other forums. I haven't plagarized anyone, they are my own words, but I will try and reword all of that stuff to make it right and not do it again. My forum can be found at this link:
The Pathway Machine
I always found the discrepancy in Biblical genealogies to be interesting. So far I have yet to see a reasonable explanation of the following.
Genealogies of Chronicles and Luke
1 Chronicles 1:17-18
17 The sons of Shem: Elam, Asshur, Arpachshad, Lud, and Aram. And the sons of Aram:[d] Uz, Hul, Gether, and Meshech. 18Arpachshad fathered Shelah, and Shelah fathered Eber.
Luke 3:35-36
35the son of Serug, the son of Reu, the son of Peleg, the son of Eber, the son of Shelah, 36the son of Cainan, the son of Arphaxad, the son of Shem, the son of Noah, the son of Lamech,
Putting the two lists in descending order it's easier to see the flaw.
Chronicles 1:17-18         Luke 3:35-36
Noah                    Noah
Shem                   Shem
Arpachshad               Arphaxad
                       Cainan
Shelah                   Shelah
Eber                     Eber
Explanation Of Difficulties In The Genealogies Of Matthew And Luke
The first chapter of Matthew the genealogy of Jesus runs from Abraham forward. In Luke chapter 3 the genealogy goes back to "Adam son of God." Part of Jesus genealogy also appears at 1 Chronicles chapters 1 - 3, running from Adam through Solomon and Zerubbabel. The books of Genesis and Ruth combined give the line from Adam to David.
The latter three lists - Genesis/Ruth, 1 Chronicles and Luke - agree fully from Adam to Arpachshad, with minor differences on certain names such as Kenan, which is "Cainan" at Luke 3:37. The Chronicles and Genesis/Ruth lists agree down to David while another "Cainan" is found in Luke's account between Arpachshad and Shelah. (Luke 3:35-36)
From Solomon to Zerubbabel the Chronicles record and Matthew agree though Matthew omits some names. One needs to address these as well as the differences in Luke's account from David to Jesus.
Genealogy involved private family records in addition to the public records of genealogies which chroniclers, such as Ezra, for example, had access to when they compiled their lists. To the registers that existed in the first century up until 70 C.E. the matter of the descent of the Messiah from Abraham through David was very important.
Matthew and Luke no doubt consulted these genealogical tables.
The question is why does Matthew leave out some names that are contained in the listing of other chroniclers? For one thing it is not necessary to name every link in the line of descent. Ezra, for example, in proving his priestly lineage, at Ezra 7:1-5, left out several names that were listed at 1 Chronicles 6:1-15. Matthew seems to have copied from the public register - leaving out some names not needed to prove the descent of Jesus from Abraham and David. Access of the Hebrew Scriptures would have likely been used as well. (Ruth 4:12, 18-22 and Matthew 1:3-6)
Both the lists made by Matthew and Luke would have been publicly recognized by the Jews of that time as authentic. The Pharisees as well as the Sadducees - bitter enemies of Christianity didn't challenge these genealogies. They could have done so up until 70 C.E. when the records were destroyed in the destruction of Jerusalem.
Problems in Matthew's Genealogy?
Matthew divides the genealogy from Abraham to Jesus into three sections of 14 generations each. There is a name count of 41 rather than 42. By taking Abraham to David, 14 names, then using David as the starting name for the second 14, with Josiah as the last and finally by heading the third series of 14 names with Jeconiah (Jehoiachin) and ending with Jesus. Matthew repeats the name David as the last of the first 14 names and as the first of the next 14. Then he repeats the expression "the deportation to Babylon," which he links with Josiah and his sons. (Matthew 1:17)
There is an omission of three kings of David's line between Jehoram and Uzziah (Azariah) because Jehoram married wicked Athaliah of the house of Ahab, the daughter of Jezebel bringing this God condemned strain into the line of the kings of Judah. (1 Kings 21:20-26 / 2 Kings 8:25-27) Matthew named Jehoram as first in this wicked alliance, but left out the next three kings to the fourth generation - Ahaziah, Jehoash, and Amaziah.
Where Matthew indicates that Zerubbabel is the son of Shealtiel (Matthew 1:12) it coincides with other references (Ezra 3:2 / Nehemiah 12:1 / Hagai 1:14 / Luke 3:27) but at 1 Chronicles 3:19 Zerubbabel is listed as the son of Pedaiah. This is because Zarubbabel was the natural son of Pedaiah and the legal son of Shealtiel by brother-in-law marriage or possibly after Zerubbabel's father Pedaiah died Zerubbabel was brought up by Shealtiel as his son and so legally recognized as the son of Shealtiel.
Problems With Lukes Genealogy?
Available manuscript copies of Luke list a second "Cainan" between Arpachshad (Arphaxad) and Shelah. (Luke 3:35 Compare Genesis 10:24 / 11:12 / 1 Chronicles 1:18, 24) Most scholars take it to be a copyist's error. "Cainan" is not found in this position in the Hebrew genealogical listings in the Hebrew or Samaritan texts, nor in any of the Targums or versions except the Septuagint. It doesn't seem to be in earlier copies of the Septuagint because Josephus - who almost always uses the Septuagint - lists Seles (Shelah) next as the son of Arphaxades (Arpachshad) - (Jewish Antiquities, I, 146 [vi, 4]) Africanus, Irenaeus, Jerome and Eusebius all rejected "Cainan" in Luke's account as an interpolation.
Bible Lists Of Jesus' Genealogy
Genesis And Ruth - Adam, Seth, Enosh, Kenan, Mahalalel, Jered, Enoch, Methuselah, Lamech, Noah, Shem, Arpachshad, Shelah, Eber, Peleg, Reu, Serug, Nahor, Terah, Abram (Abraham), Isaac, Jacob (Israel), Judan (and Tamar), Perez, Hezron, Ram, Amminadab, Nahshon, Salmon, Boaz (and Ruth), Obed, Jesse, David.
1 Chronicles chapters 1, 2, 3. - Adam, Seth, Enosh, Kenan, Mahalalel, Jared, Enoch, Methuselah, Lamech, Noah, Shem, Arpachshad, Shelah, Eber, Peleg, Reu, Serug, Nahor, Terah, Abraham, Isaac, Jacob, Judah, Perez, Hezron, Ram, Amminadab, Nahshon, Salmon (Salma, 1 Chronicles 2:11), Boaz, Obed, Jesse, David, Solomon, Rehoboam, Abijah, Asa, Jehoshaphat, Jehoram, Ahaziah, Jehoash, Amaziah, Azariah (Uzziah), Jotham, Ahaz, Hezekiah, Amon, Josiah, Jehoiakim, Jeconiah (Jehoiachin), Shealtiel (Pedaiah) (See Footnote # 1), Zerubbabel (see Footnote # 2).
Matthew Chapter 1 - Abraham, Isaac, Jacob, Judah (and Tamur), Perez, Hezron, Ram, Amminadab, Nahshon, Salmon (and Salmon Rahab), Boaz (and Ruth), Obed, Jesse, David (and Bath-sheba), Solomon, Rehoboam, Abijah, Asa, Jehoshaphat, Jehoram, Uzziah (Azariah), Jotham, Ahaz, Hezekia, Manasseh, Amon, Josiah, Jeconiah, Shealtiel, Zerubbabel, Abiud, Eliakim, Azor, Zadok, Achim, Eliud, Eleazar, Matthan, Jacob, Jusus (foster son).
Luke chapter 3 - Adam, Seth, Enosh, Cainan, Mahalaleel, Jared, Enoch, Methuselah, Lamech, Noah, Shem, Arpachshad, Cainan, Shelah, Eber, Peleg, Reu, Serug, Nahor, Terah, Abraham, Isaac, Jacob, Judah, Perez, Hezron, Arni (Ram?), Amminadab, Nahshon, Boaz, Obed, Jesse, David, Nathan (See Footnote # 3), Mattatha, Menna, Melea, Eliakim, Jonam, Joseph, Judas, Symeon, Levi, Matthat, Jorim, Eliezer, Jesus, Er, Elmadam, Cosam, Addi, Melchi, Neri, Shealtiel (See Footnote # 4), Zerubbabel, Rhesa, Joanan, Joda, Josech, Semein, Mattathias, Maath, Naggai, Esli, Nahum, Amos, Mattathias, Joseph, Jannai, Melchi, Levi, Matthat, Heli (father of Mary), Joseph (Heli's son-in-law), Jesus (Mary's son).
Footnote # 1. Zerubbabel evidently was the natural son of Pedaiah and the legal son of Shealtiel by brother-in-law marriage; or he was brought up by Shealtiel after his father Pedaiahs death and became legally recognized as the son of Shealtiel (1 Chronicles 3:17-19 / Ezra 3:2 / Luke 3:27).
Footnote # 2. The lines meet in Shealtiel and Zerubbabel, afterward diverging. This divergence could have been through two different descendants of Zerubbabel, or Rhesa or Abiud could have been a son-in-law.
Footnote # 3. At Nathan, Luke begins reckoning the genealogy through Jesus maternal line, while Matthew continues with the paternal line.
Footnote #4. Shealtiel the son of Jeconiah possibly was the son-in-law of Neri. (1 Chronicles 3:17 / Luke 3:27).