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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. 2

%I

%S 45136,36137,10128,14267,12126,4455,10126,11197,5742,15316,17543,8305,

%T 5252,5252,12126,3852,3402,2553,4567,11117,8305,11427,6931,1017,3852,

%U 11615,1746,3375,6295,3678,5252,2363,5766,5517,1936,5528,2405,8305,1936

%N 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.

%e a(1)=m=45136 because m^2=2037258496 and n^2=1 have no common digits and together use all 10 decimal digits;

%e a(2)=m=36137 because m^2=1305882769 and n^2=4 have no common digits and together use all 10 decimal digits;

%e 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);

%e 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.

%Y A158932

%K base,nonn

%O 1,1

%A _Zak Seidov_, Mar 31 2009

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)