Are you sure you're not getting confused with the link between the dates of Shavuos and Yom Kippur? Which is: Moses went up Mt Sinai for forty days after Shavuos, then came down and found the Israelites worshiping the Golden Calf. He then went up for a further forty days to beg forgiveness, and then a third forty days, at the end of which he came down with the second set of tablets as a sign of G-d's forgiveness, which was on Yom Kippur.