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A Lychrel number is a number which never yields a palindrome in the iterative process of adding to itself a copy of itself with digits reversed. For example, if we start with the number 983 we get:
So in 3 steps we get a palindrome, hence 983 is not a Lychrel number.
In fact, it is not known if there exist any Lychrel numbers in base 10 (numbers colloquially called “Lychrel numbers” in base 10 are in fact just Lychrel candidates). However, in base 2 for example, there have been numbers proven to be Lychrel numbers 1. The first Lychrel candidate is 196:
This has been followed out to millions of digits, with no palindrome found in the sequence.
The following table gives the number of Lychrel candidates found within ascending ranges:
| Range |
Possible Lychrels |
| 0 - 100 |
0 |
| 100 - 1,000 |
2 |
| 1,000 - 10,000 |
3 |
| 10,000 - 100,000 |
69 |
| 100,000 - 1,000,000 |
99 |
| 10,000,000 - 100,000,000 |
1728 |
| 100,000,000 - 1,000,000,000 |
29,813 |
- 1
- Wade VanLandingham, 196 And Other Lychrel Numbers
- 2
- John Walker, Three Years of Computing
Footnotes
- 1
- [2] informs us that Ronald Sprague has proved that the number 10110, for example, is a Lychrel number is base 2.
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