@christianp Using Wilson's theorem, it's actually a bit simpler: add 4 at position 2 and for all other rows: primes get added at the back, non-primes at the front.
@christianp The relative ordering is stable, so... is there some sort of metric function I can define that would be deterministic for any row? Can I calculate row 1000000 independent of the previous rows?
@christianp the nth row is created by inserting n somewhere into the n-1st row. Even numbers are inserted into the left half of the row, and odd numbers are inserted into the right half of the sequence, but I haven't worked out the full rule yet.
I notice that all the even numbers always come before all the odd numbers. More than that, within each group the multiples of three come before the other numbers. Which makes me think it's a factorisation thing… but this breaks down for higher powers (4,8,2 rather than 8,4,2) and higher primes (1,7,5 rather than 5,7,1).
I want to say it's going to be something like the numbers are added to minimise some property of the sequence, and ties are broken by placing the number as early as possible?
Or the whole thing is a red herring and it's nothing to do with any of that, idk — there are all sorts of little patterns in there that break after a while 🤷
@christianp each row adds the row number somewhere into the previous row. Perhaps row n is 1..n sorted according to some rule? Not sure what yet. Good puzzle!
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