[ *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

Nothing negative!

Remember, a negative times a negative is a positive.

No one knew about sporadic reversible square numbers

that are not palindromic and without ending with zero.