A084043 Smallest palindromic multiple of n in which the digit string of n appears as sandwiched between at least a pair of digits, or 0 if n = 10k or no such number exists.

111, 222, 333, 444, 555, 666, 777, 888, 999, 0, 1111, 82128, 41314, 414414, 55155, 61616, 317713, 41814, 41914, 0, 912219, 2222, 52325, 2324232, 52525, 82628, 82728, 828828, 52925, 0, 2131312, 23232, 3333, 2243422, 535535, 2136312, 43734, 88388