ALL numbers up to 10,000 become palindromes very quickly... except for the number 196?
This is NOT true. This has been quoted incorrectly for a long time. There are about 250 numbers under 10,000 that never appear to resolve into a palindrome.
If 196 will never solve, then it is obvious that 691 will never solve. Also, it is obvious that 295, 394, 493, 592, and again 691 will never solve (what are normally called the 'consequences of 196').
The first iteration after 196, 887, will thus never solve, as well as 788. From these two number, it is obvious that 986, 887, 788, 689 will never solve (the consequences of 887).
The other lychrel sequences under 10,000 are 879, 1997, and 7059. Each of these numbers, and their sequences, and all consequences of these numbers and their sequences will also never solve.
It shows the numbers that take the longest length of time before they solve. So, they are the closest numbers to Lychrels that aren't Lychrels. It also details my section of the 196 Quest.
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If 196 will never solve, then it is obvious that 691 will never solve. Also, it is obvious that 295, 394, 493, 592, and again 691 will never solve (what are normally called the 'consequences of 196').
The first iteration after 196, 887, will thus never solve, as well as 788. From these two number, it is obvious that 986, 887, 788, 689 will never solve (the consequences of 887).
The other lychrel sequences under 10,000 are 879, 1997, and 7059. Each of these numbers, and their sequences, and all consequences of these numbers and their sequences will also never solve.
If you are interested in Lychrel numbers, my page here: http://www.jasondoucette.com/worldrecords.html
It shows the numbers that take the longest length of time before they solve. So, they are the closest numbers to Lychrels that aren't Lychrels. It also details my section of the 196 Quest.
Jason Doucette
www.jasondoucette.com