Math.
In Lois McMaster Bujold's Vorkosigan books, there is a naming system for the nobility that is rooted in Tradition, or at least the tradition of the planet in question. (Barrayar, which has vague Russian overtones, and which apparently has roots in the Klingon homeworld, but that's another matter.)
The firstborn son will take on the the first names of his grandfathers on either side, with the paternal grandfather's name as his first name, and the maternal grandfather's as his middle name. Therefore, if the child's grandfathers are Piotr Pierre Vorkosigan and Miles Mark Naismith, and Piotr Pierre Vorkosigan is his paternal grandfather, then the child's name will be Piotr Miles Vorkosigan.
(Yes, I know plot doesn't make it so, but this is just an example.)
The secondborn son will take on the names of the second (middle) names of his grandfathers on either side, but reversed: the maternal grandfather's middle name is his first name, and the paternal grandfather's is his middle name. So the secondborn grandson of the above Piotr Pierre Vorkosigan and Miles Mark Naismith would be Mark Pierre Vorkosigan.
So. How many generations would it take for there to be a Piotr Pierre after the first one? As in, the shortest number of generations, and a curious drive to see this result as efficiently as possible?
I was trying to work this out in my head, but realised that I don't actually know enough about the setting. I was assuming no marriages closer than second cousins (which darkly fits both the "backwards planet" and the "inbred nobility" stereotypes), and no more than two sons per set of parents. There isn't much about naming conventions for female offspring, which kind of makes in-setting sense considering the patriarchal system, which does get called out many many times in-universe as being backwards and stupid.
The firstborn son will take on the the first names of his grandfathers on either side, with the paternal grandfather's name as his first name, and the maternal grandfather's as his middle name. Therefore, if the child's grandfathers are Piotr Pierre Vorkosigan and Miles Mark Naismith, and Piotr Pierre Vorkosigan is his paternal grandfather, then the child's name will be Piotr Miles Vorkosigan.
(Yes, I know plot doesn't make it so, but this is just an example.)
The secondborn son will take on the names of the second (middle) names of his grandfathers on either side, but reversed: the maternal grandfather's middle name is his first name, and the paternal grandfather's is his middle name. So the secondborn grandson of the above Piotr Pierre Vorkosigan and Miles Mark Naismith would be Mark Pierre Vorkosigan.
So. How many generations would it take for there to be a Piotr Pierre after the first one? As in, the shortest number of generations, and a curious drive to see this result as efficiently as possible?
I was trying to work this out in my head, but realised that I don't actually know enough about the setting. I was assuming no marriages closer than second cousins (which darkly fits both the "backwards planet" and the "inbred nobility" stereotypes), and no more than two sons per set of parents. There isn't much about naming conventions for female offspring, which kind of makes in-setting sense considering the patriarchal system, which does get called out many many times in-universe as being backwards and stupid.