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B-Palindromes (Posted on 2004-02-25) Difficulty: 4 of 5
A b-palindrome is an integer that is a palindrome in base b.

Show how to find a number that is a b-palindrome, of at least three digits, for at least 1000 different values of b.

For example, 200 is not a 10-palindrome, but it is a 9-palindrome (242) and a 7-palindrome (404).

No Solution Yet Submitted by DJ    
Rating: 4.0000 (6 votes)

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A Solution | Comment 1 of 11

The number 2^(1002!) is a perfect power with bases 2^2=4, 2^3=8, 2^4=16, . . . . 2^1000, 2^1001, 2^1002.

Then, the number 2^(1002!)+1 is a palindrome of at least three digits in bases 2^2=4, 2^3=8, 2^4=16, . . . . 2^1000, 2^1001, 2^1002.  All of the palindromes begin with a '1', end with a '1' and all the digits in between are zeros.

Can anyone come up with a smaller number?

Edited on February 25, 2004, 3:03 pm
  Posted by Brian Smith on 2004-02-25 15:02:57

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