provable non palindromic numbers

10110

First few iterations:
stepnumber
0 10110
1 100011
2 1010100
3 1101001
4 10110100
After that this regularity appears:
N(i={2,4,...}) = "10"+repeat("1",(i+{4,5})/4)+"01"+repeat("0",(i+{6,7})/4)
N(i={5,9,13,...}) = "11"+repeat("0",(i-{2..5})/4)+"1000"+repeat("1",(i-{2..5})/4)+"01"
N(i={3,7,11,...}) = "11"+repeat("0",(i+{0..3})/4)+"010"+repeat("1",(i+{0..3})/4)+"01"
remarks: