A048301 Reading base 4 expansion from left to right, run lengths strictly increase.

0, 1, 2, 3, 5, 10, 15, 16, 21, 26, 31, 32, 37, 42, 47, 48, 53, 58, 63, 64, 85, 106, 127, 128, 149, 170, 191, 192, 213, 234, 255, 256, 320, 341, 362, 383, 426, 511, 512, 597, 640, 661, 682, 703, 767, 768, 853, 938, 960, 981, 1002, 1023, 1024, 1045, 1066, 1087