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Math Patterns

October 12th, 2009 by Steven Pomeroy | Filed under Math Patterns.




Math Patterns

This is the first post to the new category Math Patterns.  Here in this category, I will post many interesting math patterns; some of these are very well known, and some are obscure.  For many of these mathematical patterns, one can derive general formulas very easily by just carefully observing how the math pattern develops.  Other numeric patterns will have you pounding your head on your keyboard while trying to come up with the next number in the series.

So, I give you here the first in the series (pun intended!) of math patterns:

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 . . .

Can you see the next number in the pattern?

Here is a subset of this math pattern:

7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379 . . .

The subset above is simply all of the prime numbers in the first set.  So then, what is the pattern of the first set?  This is the set of happy numbers up to and including 379.

So what the heck is a happy number?  A happy number is happy if you take each digit in the number, square them, add the squares together, and then repeat the process with the result and then eventually get the value 1.

For example, take the number 338.  First square each digit and add them together:

9 + 9 + 64 = 82

Now repeat the process with the result (82):

64 + 4 = 68

Continue the process with 68:

36 + 64 = 100

And then with 100:

1 + 0 + 0 = 1

Here the result is 1, and thus 338 is a happy number!

So what if a number is not happy?  Interestingly, an unhappy number ends up in a cyclic loop with the pattern:

4, 16, 37, 58, 89, 145, 42, 20, 4 . . .

So is there a limit to the number of happy numbers?  Happily, there are an infinite number of happy numbers – and an infinite number of unhappy numbers as well.

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5 Responses to “Math Patterns”

  1. jukyg | 18/09/10

    what the hell i don’t understand anything!!!! I thought this was supposed to help me…

  2. admin | 18/09/10

    It’s ok Jukyg – take things one step at a time – and don’t get intimidated with the numbers….

  3. suzi | 14/11/11

    i dint understood what the rubish thing is written down

  4. lauren | 16/02/13

    this helped me so much, only website i found that could explain it – thankyou so much!

  5. Math Tricks | 16/02/13

    Glad to be of help, Lauren :)

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