A098174 Smallest e>0 such that the initial digit of n^e = 1 in decimal representation.

1, 4, 9, 2, 3, 4, 5, 8, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 3, 3, 3, 3, 5, 7, 9, 25, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 16, 18, 20, 23, 27, 32, 40, 53