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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.

REFERENCES

M. Kraitchik, Mathematical Recreations, p. 48, Problem 12. - From N. J. A. Sloane, Mar 15 2013

LINKS

Table of n, a(n) for n=1..22.

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 *)

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 March 25 01:30 EDT 2017. Contains 284036 sequences.