Numbers not a multiple of 10 whose reciprocals have a palindromic repeating part.
3, 9, 15, 18, 45, 225, 1125
1
It appears that this sequence is complete.
T. D. Noe, Plot of 7 terms
Wikipedia, Repeating decimal
(Mma) Select[Range[1200], (r = RealDigits[1/#, 10]; Mod[#, 10] > 0 && ! IntegerQ[r[[1,1]]] && r[[1,1]] == Reverse[r[[1,1]]]) &]
nonn,base,nice
T. D. Noe, Jun 01 2016