Tuesday, March 10, 2015

"HAPPY NUMBERS"


Who in their right mind, ever wonders if a number is happy, is a happy number, or an unhappy number??

For God's sake I guess, there are happy numbers.
That must mean that there 
are "UNHAPPY NUMBERS", too.
{who cares}

Let's see?:  
From Wikipedia, this on "Happy Numbers":
A happy number is a number defined by the following process: 

Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers.  More formally, given a number n=n0, define a sequence n1, n2
, ... where n{i+1} is the sum of the squares of the digits of ni.Then n is happy if and only if there exists i such that ni = 1.

GOT THAT??  SOMETHING EXTRA TO BE MINDFUL OF, AS YOU DRIVE TO WORK~
If a number is happy, then all members of its sequence are happy;
if a number is unhappy, all members of the sequence are unhappy.
likewise, if your wife is happy/unhappy, all members of your marriage will be ...

Say Whut??  That takes too much time to find happiness in life, much less fap-happy numbers, IMHO.

So, 103 is a happy number.... It's also a prime number, does that make any difference? 
The 143 happy numbers up to 1,000 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, 490, 496, 536, 556, 563, 565, 566, 608, 617, 622, 623, 632, 635, 637, 638, 644, 649, 653, 655, 656, 665, 671, 673, 680, 683, 694, 700, 709, 716, 736, 739, 748, 761, 763, 784, 790, 793, 802, 806, 818, 820, 833, 836, 847, 860, 863, 874, 881, 888, 899, 901, 904, 907, 910, 912, 913, 921, 923, 931, 932, 937, 940, 946, 964, 970, 973, 989, 998, 1000 

And Iff, God Forbid, n is not happy, then its sequence does not go to 1. Instead, it ends in the cycle:
4, 16, 37, 58, 89, 145, 42, 20, 4, ...

To see this fact, first note that if n has m digits, then the sum of the squares of its digits is at most 92 m, or 81m.



Then the world ends, violently, with seawater covering us all with man-eating squids.

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