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 A059930 Numbers n such that n and n^2 combined use different digits. 5

%I

%S 2,3,4,7,8,9,17,18,24,29,53,54,57,59,72,79,84,209,259,567,807,854

%N Numbers n such that n and n^2 combined use different digits.

%C There are exactly 22 solutions in base 10.

%D M. Kraitchik, Mathematical Recreations, p. 48, Problem 12. - From _N. J. A. Sloane_, Mar 15 2013

%p # Maple program from _N. J. A. Sloane_, Mar 15 2013:

%p M:=1000;

%p a1:=[]; a2:=[];

%p for n from 1 to M do

%p # are digits of n and n^2 distinct?

%p t1:=convert(n,base,10);

%p t2:=convert(n^2,base,10);

%p s3:={op(t1),op(t2)};

%p if nops(t1)+nops(t2) = nops(s3) then a1:=[op(a1),n]; a2:=[op(a2),n^2]; fi;

%p od:

%p a1; a2;

%t Select[Range[10000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ], IntegerDigits[ #^2]]] == Length[IntegerDigits[ # ]] + Length[IntegerDigits[ #^2]] &] - _Tanya Khovanova_, Dec 25 2006

%Y Cf. A059931, A029783.

%Y Cf. A029783 = Digits of n are not present in n^2, A112736 = numbers whose squares are exclusionary.

%K nonn,base,fini,full

%O 1,1

%A _Patrick De Geest_, Feb 15 2001.

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