https://math.stackexchange.com/questions/2889876/does-there-exist-a-0-such-that-a-n-n-0-infty-is-unbounded

a0 for which the statement holds up to 1000

22, 24, 44, 56, 58, 60, 68, 80, 81, 86, 88, 90, 94, 96, 104, 106, 108, 119, 121, 122, 124, 126, 130, 132, 134, 136, 138, 140, 152, 154, 156, 158, 160, 166, 168, 169, 170, 172, 182, 188, 192, 194, 196, 198, 202, 204, 206, 208, 212, 214, 216, 218, 220, 222, 226, 228, 230, 232, 238, 240, 244, 248, 252, 266, 268, 270, 282, 284, 287, 289, 290, 292, 294, 302, 304, 306, 310, 312, 322, 326, 328, 330, 332, 340, 346, 348, 352, 358, 360, 361, 362, 364, 368, 370, 372, 378, 380, 386, 388, 390, 394, 396, 404, 412, 416, 420, 428, 432, 436, 441, 446, 448, 454, 456, 458, 460, 462, 464, 466, 468, 472, 474, 476, 478, 480, 486, 488, 490, 492, 494, 496, 500, 502, 504, 508, 510, 520, 522, 524, 532, 538, 540, 542, 544, 548, 550, 552, 554, 556, 558, 559, 561, 562, 564, 566, 568, 572, 580, 584, 586, 588, 592, 596, 600, 604, 612, 614, 616, 618, 620, 622, 623, 624, 625, 626, 628, 630, 632, 640, 642, 644, 656, 658, 660, 663, 666, 668, 672, 678, 682, 686, 690, 692, 694, 696, 698, 700, 702, 704, 710, 712, 714, 718, 720, 724, 726, 728, 729, 734, 736, 738, 740, 742, 744, 750, 754, 756, 758, 760, 766, 768, 770, 772, 774, 776, 782, 788, 790, 792, 794, 796, 802, 804, 808, 810, 814, 816, 822, 824, 826, 830, 832, 834, 838, 840, 841, 842, 844, 846, 850, 856, 860, 862, 864, 866, 868, 870, 872, 874, 876, 878, 880, 886, 888, 902, 904, 906, 908, 910, 912, 914, 916, 918, 920, 926, 928, 930, 932, 934, 936, 938, 944, 950, 952, 956, 959, 961, 962, 964, 966, 970, 972, 974, 976, 980, 982, 984, 988, 990, 998, 1000