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Wiktionary
porphyrogeniture

n. the principle of royal succession in which the first son born after his father's accession to the throne has the first claim, even if he has older brothers who were born before the father's crowning.

Wikipedia
Porphyrogeniture

Porphyrogeniture, also sometimes referred to as born to the purple, is a system of political succession that favours the rights of sons born after their father has become king or emperor, over older siblings born before their father's ascent to the throne.

Examples of this practice include Byzantium and the Nupe Kingdom. In late 11th century England and Normandy, the theory of porphyrogeniture was used by Henry I of England to justify why he, and not his older brother Robert Curthose, should inherit the throne after the death of their brother William Rufus.