A number is divisible by 3 ifand only ifthe same is true of the sum ofits digits. For example, the sum ofthe digits of n=145,373,270,099,876,790 is 87 and 87=3×29 and so n is in this case divisible by 3. Of course, we can apply the test to the number 87 itselfand indeed go on taking the sum ofdigits of the outcome at each stage until the result is obvious. Doing this for the given example produces the following sequence:
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