Definition:Lychrel Number/Candidate

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Definition

No natural number has been proved to be a Lychrel number as of time of writing (June $2017$). However, plenty of numbers have not shown themselves to terminate in a palindromic number, although in some cases millions of iterations have been tested.

Hence a candidate Lychrel number is a natural number which is not known to form a palindromic number through repeated iteration of the reverse-and add process.


Sequence

The sequence of candidate Lychrel numbers begins:

$196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978, 986, 1495, 1497, 1585, 1587, 1675, 1677, \ldots$


Also known as

Candidate Lychrel numbers are referred to as Lychrel numbers by some sources.


Historical Note

David Wells, reporting on the state of play in $1986$ in his Curious and Interesting Numbers, noted that P.C. Leyland had performed $50 \, 000$ reversals, which produced a number of over $26 \, 000$ digits, still not palindromic.

The same source reported that P. Anderson had continued the search to $70 \, 928$ digits without any success at reaching a palindrome.


By $1997$, in his Curious and Interesting Numbers, 2nd ed., he was able to report that John Walker and Tim Irvin had carried the process for $196$ to over one million digits, which was reached after $2 \, 415 \, 836$ reverse-and-add iterations, which took $3$ years of spare time on a Sun $3/260$.

They subsequently continued the work, taking the calculation to $2 \, 000 \, 000$ digits on a supercomputer, taking a mere $2$ months.

Still no sign of termination.


The term Lychrel number was coined in $2002$ by Wade VanLandingham, as a near-anagram of the name of his girlfriend Cheryl.

It's anyone's guess how to pronounce it.


Sources