Saturday, April 9, 2011

Interesting palindromic numbers

12345654321 is an interesting palindromic number, since it is the square of another palindrome: 12345654321 = 111111^2
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5 comments:

  1. muteApril 9, 2011 at 2:36 PM

    There are a lot of such numbers:
    1
    2
    3
    11
    22
    101
    111
    121
    202
    212
    1001
    1111
    2002
    10001
    10101
    10201
    11011
    11111
    11211
    20002
    20102
    100001
    101101
    110011
    111111
    200002
    1000001
    1001001
    1002001
    1010101
    1011101
    1012101
    1100011
    1101011
    1102011
    1110111
    1111111
    2000002
    2001002
    10000001
    10011001
    10100101
    10111101
    11000011
    11011011
    11100111
    11111111
    20000002
    100000001
    100010001
    100020001
    100101001
    100111001
    100121001
    101000101
    101010101
    101020101
    101101101
    101111101
    110000011
    110010011
    110020011
    110101011
    110111011
    111000111
    111010111
    111101111
    111111111
    ...

    But it's hard to prove that there are no any palindromic number X, when X^2 is palindromic too

    ReplyDelete
  2. AnonymousApril 9, 2011 at 2:57 PM

    Aren't 10...01 numbers always palindromic?

    ReplyDelete
  3. muteApril 9, 2011 at 3:01 PM

    This comment has been removed by the author.

    ReplyDelete
  4. BenVitaleApril 9, 2011 at 5:21 PM

    I posted 12345654321, because the digits are consecutive

    ReplyDelete
  5. muteApril 10, 2011 at 2:54 AM

    @BenVitale, ok.
    Squares of [1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111] have consecutive digits at all

    ReplyDelete

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