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# happy numbers pick3

Topic closed. 2 replies. Last post 4 years ago by dr san.

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bgonÃ§alves
Brasil
Member #92564
June 9, 2010
2315 Posts
Offline
 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.

United States
Member #76986
July 10, 2009
8283 Posts
Offline
 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

How you do anything is how you do everything!
bgonÃ§alves
Brasil
Member #92564
June 9, 2010
2315 Posts
Offline
 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!

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