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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
6565656565 = 9091 = 09_09_1 = 1n1n1 a pseudopalindrome (n=–1 : so 1n=10–1=09)

A000045 Prime Curios! Prime Puzzle
Wikipedia 45 Le Nombre 45 Numberland 45














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