A039299 Numbers n such that representation in base 6 has same nonzero number of 1's and 3's.

9, 19, 39, 51, 54, 56, 58, 59, 63, 69, 81, 91, 109, 114, 116, 118, 119, 121, 133, 139, 153, 163, 189, 199, 219, 231, 234, 236, 238, 239, 243, 249, 273, 291, 303, 306, 308, 310, 311, 315, 321, 324, 326, 328, 329, 333, 336, 338, 340, 341, 343, 348, 350, 352