WON plate112 | World!OfNumbers [ September 2, 2001 ] A magical blending of different conceptsin a most beautiful pattern Terry Trotter (email) and pdg We start with palindromes whose digits smoothly go down and up. These palindromes are then written out as a product of two near repdigits and unexpectedly their sum reveals the number of the beast in all his shapes. Finally we halt with the last entry which is a pandigital palindrome ! All these concepts are blended together in the following beautiful finite pattern from Terry Trotter, quite a beastly menagerie... 9 = 3 * 3 , Sum = 6 989 = 23 * 43 , Sum = 66 98789 = 223 * 443 , Sum = 666 9876789 = 2223 * 4443 , Sum = 6666 987656789 = 22223 * 44443 , Sum = 66666 98765456789 = 222223 * 444443 , Sum = 666666 9876543456789 = 2222223 * 4444443 , Sum = 6666666 987654323456789 = 22222223 * 44444443 , Sum = 66666666 98765432123456789 = 222222223 * 444444443 , Sum = 666666666 9876543210123456789 = 2222222223 * 4444444443 , Sum = 6666666666 In an effort to create an infinite pattern I (pdg) took the above palindromes p and calculated their pth palindrome (1 is the 1st palindrome). The 989th palindrome is 89098 The 98789th palindrome is 887909788 The 9876789th palindrome is 8876790976788 etc. The pattern becomes clear now from the second entry on. The pth palindrome is constructed with 88 at the outer ends and 909 in the middle. The zones inbetween are identical to the middle zone of p itself (98_767_89) ! The 98_765434567_89th palindrome is 88_765434567_909_765434567_88 The 98_7654321234567_89th palindrome is 88_7654321234567_909_7654321234567_88 The pattern holds even when the zeros start appearing in the middle. So we have e.g. The 98_7654321000001234567_89th palindrome is 88_7654321000001234567_909_7654321000001234567_88 There is a Java engine for calculating the above palindromes at The Nth Positive Integer Palindrome Generator A000112 Prime Curios! Prime Puzzle Wikipedia 112 Le nombre 112
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