A069858 1/n has period 4 in base 10.
101, 202, 303, 404, 505, 606, 808, 909, 1010, 1111, 1212, 1515, 1616, 1818, 2020, 2222, 2424, 2525, 3030, 3232, 3333, 3636, 4040, 4444, 4545, 4848, 5050, 5555, 6060, 6464, 6666, 7272, 7575, 8080, 8888, 9090, 9696, 9999, 10100, 11110, 12120, 12625
Offset: 1
Examples
1212 is in the sequence since 1/1212=0.0008250825082508250825082508250....
Programs
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Mathematica
Select[Range[13000],Length[RealDigits[1/#][[1,-1]]]==4&] (* Harvey P. Dale, Jun 30 2017 *)
Formula
Numbers of the form a*b*c where a is in {101, 303, 909, 1111, 3333, 9999}, b is a power of 2 and c is a power of 5.