The reverse and add process, if repeated will often reach a palindrome. In base 10 it is unknown whether numbers exist that do not eventually reach a palindrome (196 is the smallest current candidate in base ten.)
In binary, however, there are numbers that never reach a palindrome. Find the smallest such number and prove it never reaches a palindrome.
(In reply to
Smallest? by Jer)
It was easy enough to check that the process terminates for all smaller integers:
1 => 10 => 11
2 => 11
3 => 110 => 1001
4 => 101
5 => 1010 => 1111
6 => 1001
7 => 1110 => 10101
8 => 1001
9 => 10010 => 11011
10 => 1111
11 => 11000 => 11011
12 => 1111
13 => 11000 => 11011
14 => 10101
15 => 11110 => 101101
16 => 10001
17 => 100010 => 110011
18 => 11011
19 => 101100 => 111001 => 1100000 => 1100011
20 => 11001 => 101100 => 111001 => 1100000 => 1100011
21 => 101010 => 111111
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Posted by tomarken
on 2021-05-03 09:03:54 |
re: Smallest?
