A018884 - OEIS

%I #32 Feb 16 2025 08:32:33

%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="https://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_