This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
123 is a member as all the five cyclic permutations of 123^2 are :
{15129, 51291, 12915, 29151, 91512};
15129 = 123*123 ;
51291 = 123*417 ;
12915 = 123*105 ;
29151 = 123*237 ;
91512 = 123*744.
with(numtheory):for n from 1 to 100000 do:n0:=n^2:l:=length(n0) :ind:=0:for j from 1 to l do:s:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+ u*10^m:od:s:=floor(s-u*10^l+u):if irem(s, n)=0 then ind:=ind+1:n0:=s:else fi: od:if ind=l then printf(`%d, `, n):else fi: od:
Select[Range[900000],And@@Divisible[FromDigits/@Table[ RotateRight[ IntegerDigits[ #^2], n],{n,IntegerLength[#^2]}],#]&] (* Harvey P. Dale, Jul 31 2013 *)
def cycle(x): return (cp(x) for cp in CyclicPermutationGroup(len(x))) is_A178028 = lambda n: all(n.divides(Integer(cx,base=10)) for cx in cycle(str(n**2))) # D. S. McNeil, Jan 08 2011
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