A089337 a(1) = 1; for n>1, a(n) is the smallest, either a divisor or a multiple in that priority (order), of a(n-1) such that it is a distinct palindrome not included earlier.

1, 2, 4, 8, 88, 11, 22, 44, 484, 121, 242, 2662, 1331, 3993, 3, 6, 66, 33, 99, 9, 171, 1881, 171171, 7, 77, 616, 6776, 88088, 1001, 2002, 4004, 8008, 232232, 232, 464, 42224, 21112, 63336, 696, 25752, 111, 222, 444, 888, 21312, 333, 666, 24642, 12321, 36963