Editing Lychrel number (section)

==Other bases==
In [[Binary number|base 2]], 10110 (22 in decimal) has been proven to be a Lychrel number, since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after 4''n'' steps it reaches a number consisting of 10, followed by ''n''&nbsp;+&thinsp;1 ones, followed by 01, followed by ''n''&nbsp;+&thinsp;1 zeros.  This number obviously cannot be a palindrome, and none of the other numbers in the sequence are palindromes.

Lychrel numbers have been proven to exist in the following bases: 11, 17, 20, 26, and all powers of 2.<ref>See comment section in {{OEIS2C|id=A060382}}</ref><ref>{{cite web |title= Digit Reversal Sums Leading to Palindromes |url=http://www.mathpages.com/home/kmath004/kmath004.htm}}</ref><ref>{{cite web |title=Letter from David Seal |url=http://www.mathpages.com/home/dseal.htm |access-date=2017-03-08 |archive-url=https://web.archive.org/web/20130530003702/http://mathpages.com/home/dseal.HTM |archive-date=2013-05-30 |url-status=dead }}</ref>

No base contains any Lychrel numbers smaller than the base. In fact, in any given base ''b'', no single-digit number takes more than two iterations to form a palindrome. For ''b'' > 4, if ''k'' < ''b''/2 then ''k'' becomes palindromic after one iteration: ''k'' + ''k'' = 2''k'', which is single-digit in base ''b'' (and thus a palindrome). If ''k'' > ''b''/2, ''k'' becomes palindromic after two iterations.

The smallest number in each base which could possibly be a Lychrel number are {{OEIS|id=A060382}}:
{|class="wikitable"
|-
!''b''
!Smallest possible Lychrel number in base ''b''<br />written in base ''b'' (base 10)
|-
|2
|10110<ref>Proven to be a Lychrel Number, see {{OEIS|id=A060382}}</ref> (22)
|-
|3
|10211 (103)
|-
|4
|10202 (290)
|-
|5
|10313 (708)
|-
|6
|4555 (1079)
|-
|7
|10513 (2656)
|-
|8
|1775 (1021)
|-
|9
|728 (593)
|-
|10
|196 (196)
|-
|11
|83A (1011)
|-
|12
|179 (237)
|-
|13
|12CA (2701)
|-
|14
|1BB (361)
|-
|15
|1EC (447)
|-
|16
|19D (413)
|-
|17
|B6G (3297)
|-
|18
|1AF (519)
|-
|19
|HI (341)
|-
|20
|IJ (379)
|-
|21
|1CI (711)
|-
|22
|KL (461)
|-
|23
|LM (505)
|-
|24
|MN (551)
|-
|25
|1FM (1022)
|-
|26
|OP (649)
|-
|27
|PQ (701)
|-
|28
|QR (755)
|-
|29
|RS (811)
|-
|30
|ST (869)
|-
|31
|TU (929)
|-
|32
|UV (991)
|-
|33
|VW (1055)
|-
|34
|1IV (1799)
|-
|35
|1JW (1922)
|-
|36
|YZ (1259)
|}