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automorphic numbers
A number n such that n2 ends with the digits of n. more

The automorphic numbers up to 1015 :

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 27 values, from 1 to 740081787109376).

n\r 0  1 
21215 2 
37119 3 
4111510 4 
51413000 5 
6463356 6 
71445454 7 
81014001110 8 
9010354455 9 
10010001412000 10 
1114331331323

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.