A018884 Squares using at most two distinct digits, not ending in 0.

1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 144, 225, 441, 484, 676, 1444, 7744, 11881, 29929, 44944, 55225, 69696, 9696996, 6661661161

Offset

1,2

Comments

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

References

Richard K. Guy, Unsolved Problems in Number Theory, Section F24 (at p. 262) (Springer-Verlag, 2d ed. 1994).

Links

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Square Number.

Mathematica

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 *)

Crossrefs

Cf. A000290, A016069, A016070, A018885.

Sequence in context: A068854 A111704 A052041 * A050749 A096599 A016073

Adjacent sequences: A018881 A018882 A018883 * A018885 A018886 A018887

Keyword

nonn,base,more,hard

Author

David W. Wilson

Status

approved