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A018884
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Squares using at most two distinct digits, not ending in 0.
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3
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1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 144, 225, 441, 484, 676, 1444, 7744, 11881, 29929, 44944, 55225, 69696, 9696996, 6661661161
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OFFSET
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1,2
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COMMENTS
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No other terms below 10^41.
The sequence is probably finite.
The two distinct digits of a term cannot both be in the set {0,2,3,7,8}. Looking at the digits (with leading zeros) of i^2 mod 10^4 for 0 <= i < 10^4 shows that there are no repunit terms > 10 and the two distinct digits of a term must be one of the following 21 pairs: '01', '04', '09', '12', '14', '16', '18', '24', '25', '29', '34', '36', '45', '46', '47', '48', '49', '56', '67', '69', '89'. - Chai Wah Wu, Apr 06 2019
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REFERENCES
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Richard K. Guy, Unsolved Problems in Number Theory, Section F24 (at p. 262) (Springer-Verlag, 2d ed. 1994).
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LINKS
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MATHEMATICA
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Flatten[Table[Select[Flatten[Table[FromDigits/@Tuples[{a, b}, n], {n, 10}]], IntegerQ[ Sqrt[#]]&], {a, 9}, {b, 9}]]//Union (* Harvey P. Dale, Sep 21 2018 *)
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CROSSREFS
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KEYWORD
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nonn,base,more,hard
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AUTHOR
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STATUS
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approved
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