;Definitions and restrictions:
'''Rare''' &nbsp; numbers are positive integers &nbsp; <big> '''n''' </big> &nbsp; where:
:::* &nbsp; <big> '''n'''     </big> &nbsp; is expressed in base ten
:::* &nbsp; <big> '''r'''     </big> &nbsp; is the reverse of &nbsp; <big> '''n''' </big> &nbsp; &nbsp; (decimal digits)
:::* &nbsp; <big> '''n'''     </big> &nbsp; must be non-palindromic &nbsp; <big>('''n''' &ne; '''r''')</big>
:::* &nbsp; <big> '''(n+r)''' </big> &nbsp; is the &nbsp; '''sum'''
:::* &nbsp; <big> '''(n-r)''' </big> &nbsp; is the &nbsp; '''difference''' &nbsp; and must be positive
:::* &nbsp; the &nbsp; '''sum''' &nbsp; and the &nbsp; '''difference''' &nbsp; must be perfect squares


;Task:
:* &nbsp; find and show the first &nbsp; '''5''' &nbsp; ''rare'' &nbsp; numbers
:* &nbsp; find and show the first &nbsp; '''8''' &nbsp; ''rare'' &nbsp; numbers                     &nbsp; &nbsp; &nbsp; (''optional'')
:* &nbsp; find and show more &nbsp; ''rare'' &nbsp; numbers      &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  &nbsp;(''stretch goal'')


Show all output here, on this page.


;References:
:* &nbsp; an &nbsp; OEIS &nbsp; entry: &nbsp; [http://oeis.org/A035519 A035519 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;rare numbers].
:* &nbsp; an &nbsp; OEIS &nbsp; entry: &nbsp; [http://oeis.org/A059755 A059755 &nbsp; odd rare numbers].
:* &nbsp; planetmath entry:            &nbsp; [https://www.planetmath.org/RareNumbers rare numbers].   &nbsp; &nbsp; (some hints)
:* &nbsp; author's &nbsp;website:      &nbsp; [http://www.shyamsundergupta.com/rare.html rare numbers]  &nbsp; by Shyam Sunder Gupta. &nbsp; &nbsp; (lots of hints and some observations).
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