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happy numbers pick3

Topic closed. 2 replies. Last post 3 years ago by dr san.

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bgonçalves
Brasil
Member #92564
June 9, 2010
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Posted: June 25, 2013, 5:02 pm - IP Logged

More formally, given a number, a string Sets, ... where is the sum of the squares of the digits. So is happy if and only if there exists i such that.

Below are some examples.
7 is a happy number:
72 = 49
42 + 92 = 97
92 + 72 = 130
12 + 32 + 02 = 10
12 + 02 = 1.
If you are not happy, the sum of squares never give 1 will generate infinite terms.
4, 16, 37, 58, 89, 145, 42, 20, 4, ...
The numbers between 1 and 500 happy are:
1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338, 356, 362, 365, 367, 368, 376, 379, 383, 386, 391, 392, 397, 404, 409, 440, 446, 464, 469, 478, 487, and 490 496.

    Harve$t Moon's avatar - 5str

    United States
    Member #76986
    July 10, 2009
    8035 Posts
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    Posted: June 25, 2013, 6:05 pm - IP Logged

    More formally, given a number, a string Sets, ... where is the sum of the squares of the digits. So is happy if and only if there exists i such that.

    Below are some examples.
    7 is a happy number:
    72 = 49
    42 + 92 = 97
    92 + 72 = 130
    12 + 32 + 02 = 10
    12 + 02 = 1.
    If you are not happy, the sum of squares never give 1 will generate infinite terms.
    4, 16, 37, 58, 89, 145, 42, 20, 4, ...
    The numbers between 1 and 500 happy are:
    1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338, 356, 362, 365, 367, 368, 376, 379, 383, 386, 391, 392, 397, 404, 409, 440, 446, 464, 469, 478, 487, and 490 496.

    Thanks, dr san

    If we delete all of the repeat combinations,

    then we have only these "HAPPY" numbers.

     

    001, 007, 013, 019, 023, 028, 044, 049, 068, 079, 129, 133, 139

    167, 188, 226, 236, 239, 338, 356, 367, 368, 379, 446, 469, 478

     


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      bgonçalves
      Brasil
      Member #92564
      June 9, 2010
      2122 Posts
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      Posted: June 25, 2013, 6:10 pm - IP Logged

      Thanks, dr san

      If we delete all of the repeat combinations,

      then we have only these "HAPPY" numbers.

       

      001, 007, 013, 019, 023, 028, 044, 049, 068, 079, 129, 133, 139

      167, 188, 226, 236, 239, 338, 356, 367, 368, 379, 446, 469, 478

       


      ok! moon!