Palindromes obtained concatenating the prime factors of a Poulet number and adding to the number obtained its reversal
Marius Coman
Abstract
Marius Coman
Abstract
In this paper I make the following two conjectures: (I) There exist an infinity of Poulet numbers P such that D + R(D), where R(D) is the number obtained reversing the digits of D which is the number obtained concatenating the prime factors of P, is a palindromic number (example: such a Poulet number is P = 12801; the prime factors of 12801 are 3, 17 and 251, then D = 317251 and D + R(D) = 317251 + 152713 = 469964, a palindromic number); (II) There is no a number obtained concatenating the prime factors of a Poulet number to be a Lychrel number.
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In this paper I make the following two conjectures: (I) There exist an infinity of Poulet numbers P such that D + R(D), where R(D) is the number obtained reversing the digits of D which is the number obtained concatenating the prime factors of P, is a palindromic number (example: such a Poulet number is P = 12801; the prime factors of 12801 are 3, 17 and 251, then D = 317251 and D + R(D) = 317251 + 152713 = 469964, a palindromic number); (II) There is no a number obtained concatenating the prime factors of a Poulet number to be a Lychrel number.
Key concepts: Palindrome, Number theory, Mathematics, Infinity, Combinatorics, Prime (order theory), Prime factor, Prime number