Matthew 16: the sign of Jonas

16.4: γενεα πονηρα και μοιχαλις σημειον επιζητει και σημειον ου δοθησεται αυτη ει μη το σημειον ιωνα του προφητου και καταλιπων αυτους απηλθεν

"A wicked and adulterous generation seeketh after a sign; and there shall no sign be given unto it, but the sign of the prophet Jonas. And he left them, and departed."

16.17: 17 και αποκριθεις ο ιησους ειπεν αυτω μακαριος ει σιμων βαρ ιωνα οτι σαρξ και αιμα ουκ απεκαλυψεν σοι αλλ ο πατηρ μου ο εν τοις ουρανοις

"And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven."

Is the mention of Jonah in these passages connected? My commentaries (extremely limited as they are) suggest 16.4, that the sign of Jonas is Jesus' resurrection. Nobody connects the 2, but I wonder if there's a tie-in. Several suggest that bar-Jonah in 17 is to reinforce the contrast between knowledge learned by nature, and revealed knowledge, so to remind Peter "John/Jonah is your natural father, but my Father, etc."

I can't think of another place where Peter's parents are named. I know his mother-in-law is mentioned. What I wonder is whether this usage is parallel to Jesus being called "son of David" (Matt. 12.23 and many others). So could bar-Jonah mean "the one who has learned from Jonah," cf. back to vs. 4?

Another possible parallel that came to mind is Amos' statement (7.14-15): "Then answered Amos, and said to Amaziah, I was no prophet, neither was I a prophet's son; but I was an herdman, and a gatherer of sycamore fruit: And the LORD took me as I followed the flock, and the LORD said unto me, Go, prophesy unto my people Israel." (Per Hermann Sasse, that "a prophet's son" means the student of a prophet).

Anyone have thoughts on this?