Mathematical PalindromesDate: 01/17/97 at 19:36:43 From: Anonymous Subject: Fwd: Mathematical palindromes Do you know anything about patterns concerning mathematical palindromes and how they occur? I am doing a math project for school. I am in the 4th grade. I have discovered that if you add the reverse of a number to a number, you eventually will come to a palindrome. If they are 2-digit numbers, the sum of the 2 digits in the original number will determine the number of steps it takes to get to the palindrome. I've also found information on the palindrome 121. Are there any other patterns or facts about palindromes? I can't find much. Thank you for your help. Samantha Date: 01/18/97 at 12:00:35 From: Doctor Lynn Subject: Re: Fwd: Mathematical palindromes Dear Samantha, As far as I can tell, this is an unsolved problem of mathematics. There is no easy way to tell how many steps it will take, but I think you are right to think that with two digit numbers it is based approximately on the digit sum. Two numbers which are interesting in this field are 89 and 196. 89 takes 24 steps before it reaches a palindrome (and so does its reverse, 98), and needs a pretty powerful calculator to show the final answer. A computer program is best, but even then it needs a mathematical programming language which can cope with big numbers. 196 doesn't seem to reach a palindrome. To be more precise, about ten years ago, (the last time I heard about this) no one knew whether or not it did, so they will have tested it to thousands of steps. They may have found proof whether or not it does by now, but I haven't heard about it. With the number 121, have you noticed the pattern of squares of numbers made of rows of 1s? These are: 1: 1 11: 121 111: 12321 1111: 1234321 11111: 123454321 111111: 12345654321 etc. These are palindromes whose squares are palindromes too. I'm very pleased you're showing an interest in mathematics and I'm sorry I couldn't help more. If you are interested in number patterns, you might find the number 142857 interesting. Try multiplying it by the numbers from 1 to 7... -Doctor Lynn, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Note from the archivist: see also http://mathforum.org/dr.math/problems/barnes10.11.html , which deals a little more extensively with the unsolved problem mentioned above. |
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