It's not clear what the pattern is, so the problem can't be answered.
The strings "1234" and "4321" alternate, with certain numbers of 0's between those strings.
However, the sequence of the numbers of 0's between strings is 1, 2, 3, 5, ... -- and there is no definite pattern there.
1234 string A
0 1 zero
4321 string B
00 2 0's
1234 string A
000 3 0's
4321 string B
00000 5 0's