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 B-Palindromes (Posted on 2004-02-25)
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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 re: How many digits? Confused here. | Comment 6 of 11 |
(In reply to How many digits? Confused here. by Rawlyn)

No, it must have at least three digits in each base to count .. <i>any</i> number is a single digit when the value of the base is larger than the number itself, for an infinite number of bases.

This problem could move to the algorithms category, and instead of specifically naming 1000 in the problem, I could have said, "Given any positive integer k, how how to find a number that is a b-palindrome, of at least three digits, for at least k different values of b." I picked 1000 just as a large number to eliminate someone finding "by accident" a solution for a specific smaller number, had I chosen one.

My reference to "three digits in decimal" was referring not to the solution of the cited problem, but the simpler case of finding a value that works for only 7 digits. The point was that, while the previously offered methods do indeed work, the one I have produces substantially smaller numbers.

 Posted by DJ on 2004-02-26 20:57:22

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