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A059930
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Numbers n such that n and n^2 combined use different digits.
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5
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2, 3, 4, 7, 8, 9, 17, 18, 24, 29, 53, 54, 57, 59, 72, 79, 84, 209, 259, 567, 807, 854
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OFFSET
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1,1
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COMMENTS
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There are exactly 22 solutions in base 10.
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REFERENCES
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M. Kraitchik, Mathematical Recreations, p. 48, Problem 12. - From N. J. A. Sloane, Mar 15 2013
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LINKS
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Table of n, a(n) for n=1..22.
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MAPLE
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# Maple program from N. J. A. Sloane, Mar 15 2013:
M:=1000;
a1:=[]; a2:=[];
for n from 1 to M do
# are digits of n and n^2 distinct?
t1:=convert(n, base, 10);
t2:=convert(n^2, base, 10);
s3:={op(t1), op(t2)};
if nops(t1)+nops(t2) = nops(s3) then a1:=[op(a1), n]; a2:=[op(a2), n^2]; fi;
od:
a1; a2;
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MATHEMATICA
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Select[Range[10000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ], IntegerDigits[ #^2]]] == Length[IntegerDigits[ # ]] + Length[IntegerDigits[ #^2]] &] - Tanya Khovanova, Dec 25 2006
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CROSSREFS
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Cf. A059931, A029783.
Cf. A029783 = Digits of n are not present in n^2, A112736 = numbers whose squares are exclusionary.
Sequence in context: A058075 A029783 A112736 * A125965 A111116 A113318
Adjacent sequences: A059927 A059928 A059929 * A059931 A059932 A059933
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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Patrick De Geest, Feb 15 2001.
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STATUS
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approved
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