More digital silliness

[Bob Hearn]

Apart from cases where not all squares have the same length,
(i.e. at some moment a zero digit disappears by being rotated to the front)
such numbers seem to be very rare (none below (10^7)^2).
But it seems that even the sequence
12,14,16,21,25,31,108,122,128,129,192,196,216,221,245,247,258,294,408,463,465,486,522,604,661,694,789,804,918,933,948,981,...
or their squares
144,196,256,441,625,961,11664,14884,16384,16641,36864,38416,46656,48841,60025,61009,66564,86436,166464,214369,216225,236196,272484,364816,436921,481636,622521,646416,842724,870489,898704,962361,...

having at least one other valid square rotation does not seem to be in
OEIS but might be worth (modulo admitting "base" sequences...), since
these numbers soon become relatively rare.

Maximilian

(PARI)
for(n=1,10^8, (t=n^2)%10 |next; found=0; for(j=1,k=#Str(t)-1,
t=divrem(t,10);  /* this excludes 0's in front: */ t[2]|(t=t[1])&next;
issquare(t=t[1]+10^k*t[2])|next;
print1( if( found,"<<<", found=1;n^2)",")))