a(n) is the first number k such that the n Collatz runs starting at the consecutive numbers k, k+1, ..., k+n-1 all have the same prime-valued height while the runs starting at k-1 and k+n have nonprime heights.

A339773

a(n) is the first number k such that the n Collatz runs starting at the consecutive numbers k, k+1, ..., k+n-1 all have the same prime-valued height while the runs starting at k-1 and k+n have nonprime heights.