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Amateur Quest For Lychrel Numbers
Habberhead writes "Some people are aware of the quest for a palindromic solution for the number 196. Basically any number that doesn't form a palindrome by reversing and adding its digits is known as a Lychrel Number. (Sequence Number A023108 of Sloan's On-Line Encyclopedia of Integer Sequences) The number 196 happens to be the first of them. In over a year's worth of time, and more than 2 quadrillion calculations, this guy at www.p196.org has reversed and added the number over 100 MILLION times. His current answer is over 41 million digits long! Apparently he and a few others are also working on a distributed computing program for finding larger and larger Lychrel Numbers. It looks like they have in mind a Seti@Home style program with visible results."
does someone want to explain this in layman's terms?
Pick a number, any number. Reverse the digits in the number, add those reversed digits to the original number. Does this sum create a palindrome? If not, repeat the process with the new sum. By example:
87+78 = 165
165+651 = 726
726+627 = 1353
1353+3531 = 4884, a palindrome!
This article is saying that for the thousands of numbers tested, every one except 196 has exhibited this property.
I posted to
I posted a story a week ago about the prime number problem being solved for the first time with a deterministic algorithm and it was rejected by /.
You aren't talking about this by any chance, are you?
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Oh I suppose you could make it into math if you really wanted to. but you'd have one procedure for base10 and another for other bases. An example of doing it with 4 digit numbers (you could do a Summation of you wanted to do it for n-digit numbers of course). I will be using ascii-ized syntax (% is remainder after division, ^ is raised to the power of) since most browsers do not support the HTML extensions for mathematical expressions.
Let w = input number
Let v = resulting palindrome
v = (((w/(10^0))%10)*10^3) + (((w/(10^1))%10)*10^2) + (((w/(10^2))%10)*10^1) + (((w/(10^3))%10)*10^0);
I believe that is correct for all cases. if you want to reverse the digits of something mathematically. And I didn't test it on negative values so don't try it.
Representing a digit-flip as an equations means you could apply the calculus to it and come up with interesting results.
I don't like the method used in the article because it seems like brute force, where as manipulating some equations seems more elegant.
879, 1997, and 7059 also have this property, whatever it is. The guy even explains this on his site. I wonder who he is, and why he doesn't put his name anywhere.
>> By definition the numbers 691, 887, 788, 1675, 5761, 7436, and 6347 must also have the same problem, since they're in the chain following 196.
Read the article. These numbers don't count exactly because they follow in that chain. Only the seed of a chain counts.
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