Numbers whose reciprocals have a palindromic repeating part in base 8.
7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008
1
All palindromes appear to be just one digit. These numbers appear to be 7 * 2^(i-1) for i = 1, 2, 3,….
T. D. Noe, Plot of 19 terms
Wikipedia, Repeating decimal
(Mma) Select[Range[8^4], (r = RealDigits[1/#, 8]; ! IntegerQ[r[[1, 1]]] && r[[1, 1]] == Reverse[r[[1, 1]]]) &]
nonn,base
T. D. Noe, Jun 03 2016