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The Collatz Conjecture is a infinite natural integers that takes a number as a base one and using the first result as a new base for the rest of the serie
The procedure is simple
- if the number is pair, divide it by 2
- if it's not, multiply it by 3 then add 1
Simple enough!
But it's better having a example
The french Wikipedia page have a example with 14 as the base.
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14 is a pair
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which give us 7 since 7*2 = 14
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7 is a odd one
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which give us 22
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22 is a pair
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which give us 11 since 11*2 = 22
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11 is a odd one
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which give us 34
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34 is a pair
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which give us 17 since 17*2 = 34
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17 is a odd one
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which give us 52
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52 is a pair
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which give us 26 since 26*2 = 52
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26 is a pair
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which give us 13 since 13*2 = 26
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13 is a odd one
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which give us 40
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40 is a pair
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which give us 20 since 20*2 = 40
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20 is a pair
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which give us 10 since 10*2 = 20
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10 is a pair
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which give us 5 since 5*2 = 10
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5 is a odd one
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which give us 16
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16 is a pair
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which give us 8 since 8*2 = 16
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8 is a pair
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which give us 4 since 4*2 = 8
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4 is a pair
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which give us 2 since 2*2 = 4
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2 is a pair
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which give us 1 since 1*2 = 2
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1 is a odd one
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which give us 4
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4 is a pair
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which give us 2 since 2*2 = 4
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2 is a pair
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which give us 1 since 1*2 = 2
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1 is a odd one
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which give us 4
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4 is a pair
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which give us 2 since 2*2 = 4
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2 is a pair
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which give us 1 since 1*2 = 2
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1 is a odd one
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which give us 4
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4 is a pair
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which give us 2 since 2*2 = 4
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2 is a pair
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which give us 1 since 1*2 = 2
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1 is a odd one
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which give us 4
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And it goes on and on...
We have here a infinite repetition of 4, 2 and 1.
Here's the graphical representation of it (taking our first number account (14))
In this case, it's useless to go further since we will only produce a infinitely long string of 4s, 2s and 1s