A046294 2^a(n) contains 2^8=256 as largest proper substring of form 2^n.

108, 146, 161, 191, 208, 222, 230, 249, 258, 260, 272, 308, 313, 322, 325, 332, 350, 358, 381, 386, 389, 391, 401, 408, 416, 422, 430, 464, 470, 484, 487, 500, 508, 525, 533, 534, 541, 547, 560, 583, 587, 599, 608, 615, 628, 641, 649, 653, 663, 676, 689