How can we find the seed from a given palindrome?

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SUMMARY

The discussion centers on the process of generating palindromes from integers by adding the integer to its reversed digits. Participants explore the concept of "seeds," which are the initial integers used in this process. Notably, examples such as 56 and 57 illustrate how quickly they reach palindromic forms, while larger numbers like 10,911 demonstrate the complexity involved, reaching a palindrome after 55 iterations. The conversation also touches on the notion of Lychrel numbers, suggesting that many integers may not yield palindromes through this method.

PREREQUISITES
  • Understanding of integer manipulation and basic arithmetic operations.
  • Familiarity with the concept of palindromes in mathematics.
  • Knowledge of Lychrel numbers and their implications in number theory.
  • Basic programming skills for implementing algorithms to automate the palindrome generation process.
NEXT STEPS
  • Research the properties of Lychrel numbers and their significance in number theory.
  • Implement a Python script to automate the process of generating palindromes from seeds.
  • Explore the mathematical proof or theories surrounding the convergence of integers to palindromes.
  • Investigate the behavior of larger integers in relation to palindrome generation and Lychrel numbers.
USEFUL FOR

Mathematicians, computer scientists, and hobbyists interested in number theory, palindrome generation, and algorithm development will benefit from this discussion.

rsala004
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not really math but wondering if someone is clever enough to know answer to this..

Some of you may know that if you pick (almost) any integer and add its reversed digits to it, and repeat this process ..you will eventually get a palindrome.

for example:
# 56 becomes palindromic after one iteration: 56+65 = 121.
# 57 becomes palindromic after two iterations: 57+75 = 132, 132+231 = 363.
# 10,911 reaches the palindrome 4668731596684224866951378664 after 55 steps
(http://en.wikipedia.org/wiki/Lychrel_number)

If we call the numbers we start with as "seeds" ...we can easily produce a palindrome given (almost) any seed.

How do we extract a seed from a given palindrome?
(note that all intermediate steps count as seeds..so you only need to go back "1 step")

any ideas?
 
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rsala004 said:
if you pick (almost) any integer and add its reversed digits to it, and repeat this process ..you will eventually get a palindrome.

Actually, I would expect the opposite: that almost all numbers are 'Lychrel' numbers. I think looking at 1-10 digit numbers gives us a bad feeling for their asymptotic behavior, since ,ost numbers are large.
 

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