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PUZZLET 193

A Repeating Series from a PanDigital

The integer 123456789 is used to form a series.  The next term is generated like this:

Add all the digits together, giving 45. Add the digits together again to get 9. As soon as a single-digit sum is obtained, it becomes the first digit of the next term.

The rest of the term is simply the first eight digits of the previous term. So the series generated is:

123456789, 912345678, 991234567 . . .

Will the first term ever be repeated and, if so, after how many iterations?

series


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