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[ 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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