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%I #6 Jun 17 2016 11:27:51
%S 1,1,1,1,1,1,1,2,1,6,5,9,3,2,1,4,4,2,6,1,3,2,1,3,5,3,3,2,2,1,4,14,31,
%T 25,13,23,26,8,7,19,17,4,3,2,1,11,16,9,28,14,6,11,4,3,8,12,9,19,19,16,
%U 5,3,13,2,21,18,23,8,22,4,5,12,14,5,16,13,14,1,7,118,5,7,8,2,7,5,4,3,2,3,66
%N a(n) = the least positive k such that n^2 and (n+k)^2 have no common digits, or 0 if no such k exists.
%C a(n)=1 for 18 values of n = sqrt(A068802);
%C for n<=1000, a(n)=0 for 22 values of n:
%C 304,353,364,403,407,442,443,463,508,514,589,593,629,634,661,704,736,737,778, 805,807,818.
%C a(304)=0 because 304^2=92416 and no square can avoid one of digits 1,2,4,6,9:
%C each square ends with digits 1,4,5,6, or 9 (end zero doesn't matter), and if square ends with 5, then previous digit is 2;
%C also, a(353)=0 because 353^2=124609 and no square can avoid one of the same digits 1,2,4,6,9.
%e a(0)=1 because squares 0^2=0 and (0+1)^2=1 have no common digits, a(9)=6 because squares 9^2=81 and (9+6)^2=225 have no common digits.
%t lpk[n_]:=Module[{k=1},While[ContainsAny[IntegerDigits[n^2], IntegerDigits[ (n+k)^2]], k++];k]Array[lpk,100,0] (* _Harvey P. Dale_, Jun 17 2016 *)
%Y Cf. A068802
%K base,nonn
%O 0,8
%A _Zak Seidov_, Feb 20 2009
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