Squares with No More than 2 Distinct Digits

Sequence

The sequence of square numbers which have no more than $2$ distinct digits and not ending in $0$ begins:

$1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 144, 225, 441, 484, 676, 1444, 7744, 11 \, 881, 29 \, 929, 44 \, 944, 55 \, 225, 69 \, 696, 9 \, 696 \, 996, 6 \, 661 \, 661 \, 161, \ldots$

This sequence is A018884 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

It is not known whether there are any more.

Historical Note

Writing in $1997$, David Wells reports in his Curious and Interesting Numbers, 2nd ed. attributes the largest known square numbers which has no more than $2$ distinct (non-zero) digits, $6\,661\,661\,161$, to Yoshigahara.

It is assumed that this is the renowned puzzler Nobuyuki Yoshigahara.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6,661,661,161$