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automorphic numbers
A number  $n$  is called automorphic if  $n^2$  ends with  $n$.

For example, 376 is automorphic since  $376^2 = 141\underline{376}$.

The first automorphic numbers are 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of automorphic numbers

A graph displaying how many automorphic numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of automorphic numbers
Useful links Mathworld, Automorphic Number
Wikipedia, Automorphic number
OEIS, Sequence A003226
Automorphic numbers can also be... (you may click on names or numbers and on + to get more values)

aban 25 76 376 625 abundant 7109376 alternating 25 76 amenable 25 76 376 625 9376 90625 109376 890625 2890625 7109376 12890625 87109376 212890625 787109376 apocalyptic 9376 arithmetic 376 90625 2890625 brilliant 25 c.octagonal 25 625 8212890625 c.pentagonal 76 c.square 25 canyon 625 congruent 376 90625 109376 Cullen 25 d-powerful 376 deficient 25 76 376 625 9376 90625 109376 890625 2890625 dig.balanced 625 Duffinian 25 625 2890625 economical 25 625 90625 109376 890625 2890625 7109376 12890625 equidigital 25 109376 7109376 esthetic 76 evil 9376 7109376 12890625 87109376 212890625 Friedman 25 625 frugal 625 90625 890625 2890625 12890625 212890625 gapful 109376 2890625 12890625 212890625 1787109376 happy 376 109376 Harshad 12890625 787109376 idoneal 25 interprime 76 376 625 90625 7109376 junction 90625 890625 2890625 katadrome 76 Lucas 76 lucky 25 90625 magnanimous 25 76 376 625 metadrome 25 mountain 376 nialpdrome 76 oban 25 76 376 625 odious 25 76 376 625 90625 109376 890625 2890625 787109376 pentagonal 376 pernicious 25 76 376 625 90625 109376 plaindrome 25 power 25 625 8212890625 powerful 25 625 8212890625 Proth 25 90625 Ruth-Aaron 25 self 9376 semiprime 25 sliding 25 square 25 625 8212890625 tau 376 625 trimorphic 25 76 376 625 9376 90625 109376 890625 2890625 7109376 + 40081787109376 59918212890625 259918212890625 740081787109376 uban 25 76 unprimeable 625 90625 890625 untouchable 9376 wasteful 76 376 9376