Scholars encounter a number of problems in constructing accurate biblical chronologies. Jonathan Goldstein included this pertinent comment in his I Maccabees: A New Translation with Introduction and Commentary:
“It may seem strange that our author could use dates on two different bases. Stranger still, our author appears to have been led into error by the inconsistency of his two sets of dates, as if he himself was unaware of the difference between them. Bickerman saw the solution: similar inconsistencies are found in many ancient writers of history, when they draw on two sources which use different systems of chronology. Our author would thus be shown to have drawn on at least two sources, on a non-Jewish work dealing with Seleucid history which dated according to the Macedonian Selecuid era, and on Jewish records or traditions which dated according to the Babylonian Seleucid era.”[i]
Goldstein’s comment is equally applicable to Josephus.
[i] Goldstein, (Garden City, 1976), 25.