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)
Here are the numbers from 2 through 21, processed until a binary palindrome is gained:
Again, in each line is the number in binary, its decimal equivalent and the decimal equivalent of the reversal;
10 2 1
11 3 3
11 3 3
100 4 1
101 5 5
101 5 5
110 6 3
1001 9 9
111 7 7
1000 8 1
1001 9 9
1001 9 9
1010 10 5
1111 15 15
1011 11 13
11000 24 3
11011 27 27
1100 12 3
1111 15 15
1101 13 11
11000 24 3
11011 27 27
1110 14 7
10101 21 21
1111 15 15
10000 16 1
10001 17 17
10001 17 17
10010 18 9
11011 27 27
10011 19 25
101100 44 13
111001 57 39
1100000 96 3
1100011 99 99
10100 20 5
11001 25 19
101100 44 13
111001 57 39
1100000 96 3
1100011 99 99
10101 21 21
>>
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Posted by Charlie
on 2021-05-03 09:00:07 |
re: Smallest?
