A114942 a(n) is the largest base-4 string such that the n-th number coprime to 4 does not divide any substring of a(n).
22, 3232, 312311, 33233233, 3332113312, 332121111132, 23221212122321, 3332312213121123, 333333312213223231, 33121121231232213233, 3332312112213222213313, 333333332322313223212311
Offset: 2
Examples
a(3) = 3232 (base 4) because the 3rd number coprime to 4 is 5, and 5 does not divide any substring of a(3).