[ July 2, 2017 ]
The rarity of sporadic square reversible numbers that
are not palindromic and without ending with zero
Andres 'Tush' Molina (email)

Reversing palindromic numbers are the same and reversing numbers
ending with zero makes the zeroes cancel out and numbers cannot
start with zero.

Most reversible square numbers that are not palindromic and without
ending with zero are regular that means that its roots are
n and n reversed
and adding zeroes between the digits generates also square numbers.
( See table at wonplate 192 for examples ).

144 square root is 12 and 441 square root is 21.
169 square root is 13 and 961 square root is 31.
Add zeroes between the digits.
10404 square root is 102 and 40401 square root is 201.
10609 square root is 103 and 90601 square root is 301.

Palindromic squares are 1, 4, 9, 121, 484, 676, 10201...
Add zeroes between the digits.
10201 square root is 101, 40804 square root is 202,
60706 is not a square number because 676 is a sporadic square number.

Since numbers ending with 0 are divisible by 10, 10 is squarefree
and not divisible by a square number besides 1. Square numbers
that end with 0 always end with the even number of zeroes.

Sporadic reversible square numbers that are not palindromic
and without ending with zero are much rarer than sporadic square
numbers, sporadic reversible square numbers ending with zero and
regular reversible square numbers that are not palindromic and
without ending with zero.

According to the palindromic square numbers whose roots is
pseudo-palindromic, 091=1n1 and n=-1. The smallest pseudo-regular
reversible square number is 12303690084 and its root is 110922
or 111n22 that is pseudo-reversal with 219111 or 22n111.

  +1+1+1-1+2+2
x +1+1+1-1+2+2
--------------
  +1+1+1-1+2+2
  ..+1+1+1-1+2+2
  ....+1+1+1-1+2+2
  ......-1-1-1+1-2-2
  ........+2+2+2-2+4+4
  ..........+2+2+2-2+4+4
------------------------
  +1+2+3+0+3+6+9+0+0+8+4

No one knew about sporadic reversible square numbers
that are not palindromic and without ending with zero.