WON TOPIC 45

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Some beautiful patterns resulting in palindromes 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 1n1n1 is a pseudopalindrome ( n = –1 hence 1n = 10–1 = 09 )
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