the son of Serug, the son of Reu, the son of Peleg, the son of Eber, the son of Shelah
Another solution is that Matthew provided a list of incumbents (actual or potential) to the Davidic throne, and Luke listed Joseph’s physical father and forefathers. [Note: Machen, p. 209; The New Bible Dictionary, 1962 ed., s.v. "Genealogy of Jesus Christ," by F. F. Bruce.] I prefer this view. According to this view Matthew showed that Jesus had a legitimate right to rule as Messiah since He was in the royal line through His legal guardian Joseph. Luke showed that Jesus was a real blood descendant of David. Yet Luke had already showed in chapters 1 and 2 that Jesus was not a biological son of Joseph. Advocates of this view point out that Luke was careful to state that Jesus was only supposedly the son of Joseph (Luke 3:23). However if He was not the physical son of Joseph what is the point of tracing Joseph’s ancestors to prove Jesus’ humanity? This criticism applies to the former view too. Probably in the eyes of Greeks Jesus’ connection with Adam through Joseph would have been adequately convincing.