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 A059930 Numbers n such that n and n^2 combined use different digits. 5
 2, 3, 4, 7, 8, 9, 17, 18, 24, 29, 53, 54, 57, 59, 72, 79, 84, 209, 259, 567, 807, 854 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are exactly 22 solutions in base 10. More precisely: the concatenation of n and n^2 does not contain any digit twice. - M. F. Hasler, Oct 16 2018 REFERENCES M. Kraitchik, Mathematical Recreations, p. 48, Problem 12. - From N. J. A. Sloane, Mar 15 2013 LINKS MAPLE 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; # N. J. A. Sloane, Mar 15 2013 MATHEMATICA Select[Range[10000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ], IntegerDigits[ #^2]]] == Length[IntegerDigits[ # ]] + Length[IntegerDigits[ #^2]] &] (* Tanya Khovanova, Dec 25 2006 *) Select[Range[10^3], Union@ Tally[Flatten@ IntegerDigits@ {#, #^2}][[All, -1]] == {1} &] (* Michael De Vlieger, Oct 17 2018 *) PROG (PARI) select( is(n)=#Set(Vecsmall(n=Str(n, n^2)))==#n, [1..999]) \\ M. F. Hasler, Oct 16 2018 CROSSREFS Cf. A059931, A029783 (digits of n are not present in n^2), A112736 (numbers whose squares are exclusionary). Sequence in context: A243495 A029783 A112736 * A125965 A111116 A113318 Adjacent sequences:  A059927 A059928 A059929 * A059931 A059932 A059933 KEYWORD nonn,base,fini,full AUTHOR Patrick De Geest, Feb 15 2001 STATUS approved

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Last modified October 20 02:09 EDT 2019. Contains 328244 sequences. (Running on oeis4.)