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What is the next number in the following sequence?

9999999, 4782969, 217728, 1568, ???

I saw this question in an app and I am stuck. Can you help me?
Source: https://play.google.com/store/apps/details?id=com.broli.whatsnext

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The next number is

240

And the following is

0

Because:

Each number is the product of the digits of the preceding number: 9*9*9*9*9*9*9=4782969, 4*7*8*2*9*6*9=217728, 2*1*7*7*2*8=1568, and so the next number in the sequence is 1*5*6*8=240, and finally 2*4*0=0, where the sequence ends.

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  • 7
    $\begingroup$ One way to look at it is that the sequence ends. Another way is that it goes on forever, in an incredibly boring manner. $\endgroup$ – Mooing Duck Feb 18 '15 at 1:08
  • $\begingroup$ @MooingDuck Without letting any spoilers slip, Martin Gardiner once expostulated on some interesting properties of such sequences, in particular of their lengths, which of course requires us to define the sequences to be finite. $\endgroup$ – Dan Bron Feb 18 '15 at 1:21
  • $\begingroup$ It will be interesting if the distribution of getting to a certain value from a starting number will be different than 10% $\endgroup$ – Moti Feb 18 '15 at 5:59
  • $\begingroup$ I feel like the final result for any starting value is either an endless string of 0's, or more rarely an endless string of 1's. I'm curious if there are starting values that can end in any other way, either cycling on the same number, or in a repeating chain of some sort. $\endgroup$ – Darrel Hoffman Apr 20 '16 at 15:05
  • $\begingroup$ @DarrelHoffman I think it could end as an endless string of any single digit, 0 being the most likely. If you only use positive integers I can't think of how it would cycle because I can't think of how it could ever increase. $\endgroup$ – 182764125216 Aug 29 '16 at 14:41

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