In mathematics an automorphic number (sometimes referred to as a circular number) is a number whose square "ends" in the same digits as the number itself. For example, 52 = 25, 62 = 36, 762 = 5776, 3762 = 141376,and 8906252 = 793212890625, so 5, 6, 76 and 890625 are all automorphic numbers. The terms circular and spherical were formerly used for the slightly different case of a number whose powers all have the same last digit as the number itself, the only spherical numbers being 5, 6 and 10.[1]
The only automorphic Kaprekar number is 1, because the square of a Kaprekar number cannot start with zero.
The sequence of automorphic numbers begins 1, 5, 6, 25, 76, 376, 625, 9376, ... (sequence A003226 in the OEIS).