[ May 10, 2018 ]
The discovery of new irregular non-palindromic and
without ending with zero square number reversals
Andres 'Tush' Molina (email) [ from Vail, Arizona ]

The OEIS Sequence of square number reversals, non-palindromic,
without ending with zero and irregular is A284986.

Most of the roots are pseudo-reversals and I only discovered 2 sporadic ones.
The sporadic roots are 103043953125 and 229469560449
Its square numbers are
103043953125² = 10618056275627197265625_|

229469560449² = 52656279172657265081601

Next, I also discovered the smallest pseudo-reversal with m=-2 which is
11100010811111 = 11100011m11111 and 11110811000111 = 11111m11000111

For pseudo-reversals, n=-1 and m=-2 we use
the following substitutions
1n=09, 2n=19, 3n=29, 1m=08, 2m=18
10n=099, 1nn=809, 20n=199, 2nn=189.
10m=098, 1nm=088, 1mm=078, 1mn=079,
20m=198, 2nm=188, 2mm=178, 2mn=179.

  11100011m11111
x 11100011m11111
-----------------
  11100011m11111
  .11100011m11111
  ..11100011m11111
  ......11100011m11111
  .......11100011m11111
  ........mmm000mm4mmmmm
  .........11100011m11111
  ..........11100011m11111
  ...........11100011m11111
  ............11100011m11111
  .............11100011m11111
-----------------------------
  123210240006781080121054321

123210240006781080121054321 is the smallest square number whose reversal
is also a square number but their roots are pseudo-reversal with m=-2

11100010811111² = 11100011m11111² = 123210240006781080121054321_|

11110811000111² = 11111m11000111² = 123450121080187600042012321