WON TOPIC 45

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After an exercice on Sloane's integer sequences A048611 and A048612 [ June 27, 1999 ] originally submitted by Felice Russo with description [ Least solutions for 'Difference between two squares is a repunit of length n' ] I discovered that some beautiful patterns resulting in palindromes could be constructed. 6² - 5² = 11 66² - 65² = 131 666² - 665² = 1331 6666² - 6665² = 13331 66666² - 66665² = 133331 6² - 5² = 11 56² - 45² = 1111 556² - 445² = 111111 5556² - 4445² = 11111111 55556² - 44445² = 1111111111 56² - 55² = 111 5056² - 5045² = 111111 500556² - 500445² = 111111111 50005556² - 50004445² = 111111111111 All numbers are palindromes in the next 'nec plus ultra' (one infinite and one finite) marvelous patterns! 6² - 5² = 11 656² - 565² = 111111 65656² - 56565² = 1111111111 6565656² - 5656565² = 11111111111111 6² - 5² = 11 66² - 55² = 1331 666² - 555² = 135531 6666² - 5555² = 13577531 66666² - 55555² = 1357997531 P.S. Note the following observations 65656 + 56565 = 122221 a palindrome 65656 – 56565 = 9091 = 09_09_1 = 1n1n1 a pseudopalindrome (n=–1 : so 1n=10–1=09)
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After an exercice on Sloane's integer sequences A048611 and A048612 [ June 27, 1999 ]
originally submitted by Felice Russo with description
[ Least solutions for 'Difference between two squares is a repunit of length n' ]
I discovered that some beautiful patterns resulting in palindromes could be constructed.

        6² - 5² = 11
      66² - 65² = 131
    666² - 665² = 1331
  6666² - 6665² = 13331
66666² - 66665² = 133331

        6² - 5² = 11
      56² - 45² = 1111
    556² - 445² = 111111
  5556² - 4445² = 11111111
55556² - 44445² = 1111111111

            56² - 55² = 111
        5056² - 5045² = 111111
    500556² - 500445² = 111111111
50005556² - 50004445² = 111111111111

All numbers are palindromes in the next
'nec plus ultra' (one infinite and one finite) marvelous patterns!

            6² - 5² = 11
        656² - 565² = 111111
    65656² - 56565² = 1111111111
6565656² - 5656565² = 11111111111111

        6² - 5² = 11
      66² - 55² = 1331
    666² - 555² = 135531
  6666² - 5555² = 13577531
66666² - 55555² = 1357997531

P.S. Note the following observations
65656 + 56565 = 122221 a palindrome
65656 – 56565 = 9091 = 09_09_1 = 1n1n1 a pseudopalindrome (n=–1 : so 1n=10–1=09)

A000045

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