Query: Lychrel

title: Brisure de symetrie et nombres de lychrel
abstract: Nous montrons que l'existence des nombres de Lychrel est due a une brisure de symetrie dans l'espace des nombres.

title: Conjecture that there is no a Square of an Odd Number to be as Well Lychrel Number
abstract: In this paper I make the following two conjectures: (I) There exist an infinity of squares of odd numbers n^2 such that n^2 R(n^2) where R(n^2) is the number obtained reversing the digits of n^2, is a palindromic number; (II) There is no a square of an odd number to be as well Lychrel number. Note that a Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers (process sometimes called the 196 algorithm, 196 being the smallest such number) see the sequence A023108 in OEIS.

title: Conjecture that there is no a Poulet Number to be as Well Lychrel Number
abstract: In this paper I make the following two conjectures: (I) There exist an infinity of Poulet numbers P such that P R(P) where R(P) is the number obtained reversing the digits of P, is a palindromic number; (II) There is no a Poulet number to be as well Lychrel number. Note that a Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers (process sometimes called the 196 algorithm, 196 being the smallest such number) see the sequence A023108 in OEIS.

title: SECURED AND RELIABLE DATA TRANSMISSION USING LYCHREL NUMBERS RGB COLORS AND ONE TIME PASSWORD
abstract: The main objective of Securing data transmission by xml using lychrel numbers, RGB colors and one time password. The universal technique for providing Cryptography is the primary technique to assure data security. This scheme provides various factors to encrypt and decrypt the data using a key such as Lychrel numbers and RGB colors as the password. There are three keys used to provide secure and reliable data transmission with the RGB colors which is a primary security element which provides authentication. Here colors and Time based one time key are been used as the password for authentication process. Lychrel numbers are used to encrypt and then decrypt the data that is to be transmitted.

title: Three Sequences of Palindromes Obtained from Poulet Numbers
abstract: In this paper I make the following two conjectures: (I) There exist an infinity of Poulet numbers P such that (P 4*196) R(P 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 Poulet number P there exist an infinity of primes q such that the number (P 16*q^2) R(P 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 4*196) R(P 4*196) where P is a Poulet number; (2) Palindromes of the form (P 16*q^2) R(P 16*q^2) where P is a Poulet number and q the least prime for which is obtained such a palindrome; (3) Palindromes of the form (1729 16*q^2) R(1729 16*q^2) where q is prime (1729 is a well known Poulet number)

title: Three Sequences of Palindromes Obtained from Squares of Primes
abstract: 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.

title: Number P^2 Q^2 Where P and Q Primes Needs Very Few Iterations of "reverse and Add" to Reach a Palindrome
abstract: In this paper I make the following observation: the number n p^2 q^2, where p and q are primes, needs very few iterations of "reverse and add" to reach a palindrome. For instance, taking q 563 and p 104723, it can be seen that only 3 iterations are needed to reach a palindrome: n 104723^2 563^6 10966589760 and we have: 10966589760 6798566901 17765156661; 17765156661 16665156771 34430313432 and 34430313432 23431303443 57861616875, 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 squares of primes to be a Lychrel number.

title: Number P Q Where P and Q Poulet Numbers Needs Very Few Iterations of "reverse and Add" to Reach a Palindrome
abstract: 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.

title: Palindromes Obtained Concatenating the Prime Factors of a Poulet Number and Adding to the Number Obtained Its Reversal
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.

title: Secured And Reliable Data Transmission UsingLychrel Numbers Rgb Colors And One TimePassword
abstract: The main objective of Securing data transmission by xml using lychrel numbers, RGB colors and one time password. The universal technique for providing Cryptography is the primary technique to assure data security. This scheme provides various factors to encrypt and decrypt the data using a key such as Lychrel numbers and RGB colors as the password. There are three keys used to provide secure and reliable data transmission with the RGB colors which is a primary security element which provides authentication. Here colors and Time based one time key are been used as the password for authentication process. Lychrel numbers are used to encrypt and then decrypt the data that is to be transmitted.