WON plate46 | World!OfNumbers [ December 28, 1999 ] Sequel to WONplate 28 In a attempt to find the largest possible 'free of palindromic substrings' - or just palfree - numbers - except of course the single digits themselves - like for instance in the following powers : 2 54 = 18014398509481984 - 17 digits 3 67 = 92709463147897837085761925410587 - 32 digits 355 15 = 179236021709762370418314530975341796875 - 39 digits (You've other record numbers of this kind ! Please submit them to me and I'll display them here also.) Carlos B. Rivera F. sent a method to produce infinite large 'free of palindromic substrings' numbers First he gives two examples To produce the palfree number 123123123123 multiply 123 with repunit 111111111111 and divide by 111 To produce the palfree number 1234123412341234 multiply 1234 with repunit 111111111111 and divide by 1111 and then he provides the General Formula To produce N-N-N-N multiply N*R(k*n)/R(n) k = times N appears n = digits of N R(n) = (10^n–1)/(10–1) = 11....11 (n times) Is this the beginning or the end of the palfree numbers story ? A000046 Prime Curios! Prime Puzzle Wikipedia 46 Le Nombre 46 Numberland 46
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