A098953 Slowest increasing sequence where each number is such that at least one pair of adjacent digits are consecutive, the first of the pair being the smaller.

12, 23, 34, 45, 56, 67, 78, 89, 101, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 134, 145, 156, 167, 178, 189, 201, 212, 223, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 245, 256, 267, 278, 289, 301, 312, 323, 334, 340, 341