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%I #31 Dec 03 2021 02:44:44
%S 1,4,9,16,25,36,49,64,81,121,144,225,441,484,676,1444,7744,11881,
%T 29929,44944,55225,69696,9696996,6661661161
%N Squares using at most two distinct digits, not ending in 0.
%C No other terms below 10^41.
%C The sequence is probably finite.
%C 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
%D Richard K. Guy, Unsolved Problems in Number Theory, Section F24 (at p. 262) (Springer-Verlag, 2d ed. 1994).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number</a>.
%t 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 *)
%Y Cf. A000290, A016069, A016070, A018885.
%K nonn,base,more,hard
%O 1,2
%A _David W. Wilson_
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