Numbers whose Square is Palindromic with Even Number of Digits

Theorem
The sequence of positive integers whose square is a palindromic number with an even number of digits begins:
 * $836, 798 \, 644, 64 \, 030 \, 648, 83 \, 163 \, 115 \, 486, 6 \, 360 \, 832 \, 925 \, 898, \ldots$