What still seems to keep going over some people's heads is that the Table of Nations in Genesis is not a genealogy. It is an ethnology. It is intended to show the descent of the nations, ultimately leading to Israel and Christ.
Luke 3:
23 And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli,
24 Which was the son of Matthat, which was the son of Levi, which was the son of Melchi, which was the son of Janna, which was the son of Joseph,
25 Which was the son of Mattathias, which was the son of Amos, which was the son of Naum, which was the son of Esli, which was the son of Nagge,
26 Which was the son of Maath, which was the son of Mattathias, which was the son of Semei, which was the son of Joseph, which was the son of Juda,
27 Which was the son of Joanna, which was the son of Rhesa, which was the son of Zorobabel, which was the son of Salathiel, which was the son of Neri,
28 Which was the son of Melchi, which was the son of Addi, which was the son of Cosam, which was the son of Elmodam, which was the son of Er,
29 Which was the son of Jose, which was the son of Eliezer, which was the son of Jorim, which was the son of Matthat, which was the son of Levi,
30 Which was the son of Simeon, which was the son of Juda, which was the son of Joseph, which was the son of Jonan, which was the son of Eliakim,
31 Which was the son of Melea, which was the son of Menan, which was the son of Mattatha, which was the son of Nathan, which was the son of David,
32 Which was the son of Jesse, which was the son of Obed, which was the son of Booz, which was the son of Salmon, which was the son of Naasson,
33 Which was the son of Aminadab, which was the son of Aram, which was the son of Esrom, which was the son of Phares, which was the son of Juda,
34 Which was the son of Jacob, which was the son of Isaac, which was the son of Abraham, which was the son of Thara, which was the son of Nachor,
35 Which was the son of Saruch, which was the son of Ragau, which was the son of Phalec, which was the son of Heber, which was the son of Sala,
36 Which was the son of Cainan, which was the son of Arphaxad, which was the son of Sem, which was the son of Noe, which was the son of Lamech,
37 Which was the son of Mathusala, which was the son of Enoch, which was the son of Jared, which was the son of Maleleel, which was the son of Cainan,
38 Which was the son of Enos, which was the son of Seth, which was the son of Adam, which was the son of God.
This each says son of, however we see this as the line of Mary. Being Joseph was called the son of Heli, actually he was the son in law of Heli. If you count David back to Abraham you get 14 generations. what do we see in in Matthew 1:
16 And
Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ.
17 So all the generations
from Abraham to David are fourteen generations; and from David until the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon unto Christ are fourteen generations.
So Jacob was the Father of Joseph and Heli the father of Mary. Both lines go back to David, Joseph through Solomon and Mary through David's son Nathan. But it groups 14 generations, together in Matthew From Abraham to David, From David to the dispersment, from the Dispesrment to Christ. Now if we count back from Abraham to Adam what do we see from the Luke passage? 21 Generations back from there.
Now how does that align with the Genesis 5 list, verse 1 states, "This is the book of the generations of Adam."
3 And Adam lived an hundred and thirty years, and begat a son in his own likeness, and after his image; and called his name Seth:
(Luke 3:38) that one checks,
4 And the days of Adam after he had begotten Seth were eight hundred years: and he begat sons and daughters:
5 And all the days that Adam lived were nine hundred and thirty years: and he died.
6 And Seth lived an hundred and five years, and begat Enos:
(Luke 3:38) check
7 And Seth lived after he begat Enos eight hundred and seven years, and begat sons and daughters:
8 And all the days of Seth were nine hundred and twelve years: and he died.
9 And Enos lived ninety years, and begat Cainan:
(Luke 3:37) check
10 And Enos lived after he begat Cainan eight hundred and fifteen years, and begat sons and daughters:
11 And all the days of Enos were nine hundred and five years: and he died.
12 And Cainan lived seventy years and begat Mahalaleel:
(Luke 3:37) check
13 And Cainan lived after he begat Mahalaleel eight hundred and forty years, and begat sons and daughters:
14 And all the days of Cainan were nine hundred and ten years: and he died.
15 And Mahalaleel lived sixty and five years, and begat Jared:
(luke 3:37) check
16 And Mahalaleel lived after he begat Jared eight hundred and thirty years, and begat sons and daughters:
17 And all the days of Mahalaleel were eight hundred ninety and five years: and he died.
18 And Jared lived an hundred sixty and two years, and he begat Enoch:
(Luke 3:37) check
19 And Jared lived after he begat Enoch eight hundred years, and begat sons and daughters:
20 And all the days of Jared were nine hundred sixty and two years: and he died.
21 And Enoch lived sixty and five years, and begat Methuselah:
(Luke 3:37) Check
22 And Enoch walked with God after he begat Methuselah three hundred years, and begat sons and daughters:
23 And all the days of Enoch were three hundred sixty and five years:
24 And Enoch walked with God: and he was not; for God took him.
25 And Methuselah lived an hundred eighty and seven years, and begat Lamech.
(Luke 3:36) check
26 And Methuselah lived after he begat Lamech seven hundred eighty and two years, and begat sons and daughters:
27 And all the days of Methuselah were nine hundred sixty and nine years: and he died.
28 And Lamech lived an hundred eighty and two years, and begat a son:
29 And he called his name Noah, saying, This same shall comfort us concerning our work and toil of our hands, because of the ground which the Lord hath cursed.
(Luke 3:36) Check
30 And Lamech lived after he begat Noah five hundred ninety and five years, and begat sons and daughters:
31 And all the days of Lamech were seven hundred seventy and seven years: and he died.
32 And Noah was five hundred years old: and Noah begat Shem, Ham, and Japheth.
(Luke 3:36) check
from Adam forward to shem Genesis 5 matches Luke perfectly. These are the generations listed.