A044845 n-th positive integer having no fewer base 4 runs of even length than odd.

5, 10, 15, 16, 20, 22, 23, 26, 31, 32, 37, 40, 41, 43, 47, 48, 53, 58, 60, 61, 62, 80, 85, 90, 95, 160, 165, 170, 175, 240, 245, 250, 255, 256, 261, 266, 271, 320, 321, 322, 323, 325, 330, 335, 336, 340, 342, 343, 346, 351, 352, 357