A039369 Numbers n such that representation in base 9 has same nonzero number of 1's and 6's.

15, 55, 87, 105, 114, 123, 132, 135, 137, 138, 139, 140, 142, 143, 150, 159, 177, 217, 258, 298, 339, 379, 420, 460, 487, 495, 497, 498, 499, 500, 502, 503, 505, 514, 523, 532, 550, 559, 582, 622, 663, 703, 735, 753, 762, 771, 780, 783, 785, 786, 787, 788