WON plate45 | World!OfNumbers 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 ) A000045 Prime Curios! Prime Puzzle Wikipedia 45 Le Nombre 45 Numberland 45
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