Number Theory

   

Number P-Q Where P and Q Poulet Numbers Needs Very Few Iterations of “reverse and Add” to Reach a Palindrome

Authors: Marius Coman

In this paper I make the following observation: the number n = p – q, where p and q are Poulet numbers, needs very few iterations of “reverse and add” to reach a palindrome. For instance, taking q = 1729 and p = 999986341201, it can be seen that only 3 iterations are needed to reach a palindrome: n = 999986341201 – 1729 = 999986339472 and we have: 999986339472 + 274933689999 = 1274920029471; 1274920029471 + 1749200294721 = 3024120324192 and 3024120324192 + 2914230214203 = 5938350538395, a palindromic number. So, relying on this, I conjecture that there exist an infinity of n, even considering q and p successive, that need just one such iteration to reach a palindrome (see sequence A015976 in OEIS for these numbers) and I also conjecture that there is no a difference between two Poulet numbers to be a Lychrel number.

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Submission history

[v1] 2018-01-07 17:15:09

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