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A palindrome is a number that reads the same forward and backward. What is the smallest 5-digit palindrome in base 2 that can be expressed as a 2-digit palindrome in a different base? Give your response in base 2.​

 Dec 27, 2020
 #1
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A 2 digit palindrome in any base would have to be   x  x      as in 11  22  33  44  55  66  ....99  

            which of these is a palindrome in base 2?

(the only 5 digit base two numbers are 16-3110    palindromes include 17 21 27 31)

27      in base 2   =  11011

 

27 = 338

 Dec 27, 2020
 #2
avatar+112827 
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Guest is certainly correct.

 

Another answer is 11base 26

So

The smallest base 2 five digit palindrone is   100012     =   1710

 

\(10001_2=17_{10}=33_8=11_{26}\)

 Dec 28, 2020

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