[seqfan] smallest number which is coprime to the last three predecessors and not occurring earlier;

[Jonathan Post]

1,2,3,5,7,4,9,10,11,...

is that the right start for smallest number which is coprime to the
last three predecessors and not occurring earlier; a(1)=1, a(2)=2,
a(3) = 3?

This would be to 3 as A084937 is to 2.

It would be a permutation of the natural numbers.

Is it still true that primes occur in natural order?

Would it also have few fixed points?

-- Jonathan Vos Post