A158931 a(n) = smallest number m such that m^2 and n^2 share no common digits and m^2 and n^2 together use all 10 digits, a(n) = 0 if no such m exists.

45136, 36137, 10128, 14267, 12126, 4455, 10126, 11197, 5742, 15316, 17543, 8305, 5252, 5252, 12126, 3852, 3402, 2553, 4567, 11117, 8305, 11427, 6931, 1017, 3852, 11615, 1746, 3375, 6295, 3678, 5252, 2363, 5766, 5517, 1936, 5528, 2405, 8305, 1936

Offset: 1

Author

Zak Seidov, Mar 31 2009

Keywords

• base
• nonn

Examples

			a(1)=m=45136 because m^2=2037258496 and n^2=1 have no common digits and together use all 10 decimal digits;
a(2)=m=36137 because m^2=1305882769 and n^2=4 have no common digits and together use all 10 decimal digits;
first zero is a(304)=0 because 304^2=92416, "free" digits are {0,3,5,7,8} none of them can be last digit of square (zero can but this does not matter, also 5 can but only in combination 25 while 2 is not available for m^2);
similarly, a(353)=0 because 353^2=124609, and free digits are {3,5,7,8}. Values of n for which m=0 are in A158932.
		

Crossrefs

A158932