A044455 Numbers n such that string 3,1 occurs in the base 4 representation of n but not of n+1.

13, 29, 45, 55, 61, 77, 93, 109, 119, 125, 141, 157, 173, 183, 189, 205, 223, 237, 247, 253, 269, 285, 301, 311, 317, 333, 349, 365, 375, 381, 397, 413, 429, 439, 445, 461, 479, 493, 503, 509, 525, 541, 557, 567, 573, 589, 605