Automorphic

An automorphic number (in base 10) is a number whose square ends with the number itself. For example, 5² = 25 and 25² = 625; so 5 and 25 are automorphic.

Key features

• Only 0 and 1 are automorphic in base 10 for one digit; 5 and 6 for two digits; 25 and 76 for three; etc.
• There are two infinite sequences of base-10 automorphic numbers.

Examples:

1, 5, 6, 25, 76, 376, 625

Further reading

• Automorphic on Wikipedia
• Automorphic on OEIS