Number Theory


Three Sequences of Palindromes Obtained from Squares of Primes

Authors: Marius Coman

In this paper I make the following two conjectures: (I) There exist an infinity of squares of primes p^2 such that (p^2 + 4*196) + R(p^2 + 4*196), where R(n) is the number obtained reversing the digits of n, is a palindromic number; note that I wrote 4*196 instead 784 because 196 is a number known to be related with palindromes: is the first Lychrel number, which gives the name to the “196-algorithm”; (II) For every square of odd prime p^2 there exist an infinity of primes q such that the number (p^2 + 16*q^2) + R(p^2 + 16*q^2) is a palindrome. The three sequences (presumed infinite by the conjectures above) mentioned in title of the paper are: (1) Palindromes of the form (p^2 + 4*196) + R(p^2 + 4*196), where p^2 is a square of prime; (2) Palindromes of the form (p^2 + 16*q^2) + R(p^2 + 16*q^2), where p^2 is a square of prime and q the least prime for which is obtained such a palindrome; (3) Palindromes of the form (13^2 + 16*q^2) + R(13^2 + 16*q^2), where q is prime.

Comments: 3 Pages.

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Submission history

[v1] 2018-01-07 07:13:35

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