seq? Least k such that the length of the Roman numeral for k = the length of the binary representation of k = n

[Jonathan Post]

Okay, here's another weird one relating Roman numerals to a base.

1, 2, 7, 8, 33, 78, 138, 278, 688, 1288

Least k such that the length of the Roman numeral for k = the length
of the binary representation of k = n.

a(n) = MIN{k such that A006968(k) = A070939(k) = n}

Cf. A036787, A007088, A006968, A070939