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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1 Answer
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5
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 is1*5*6*8=240, and finally2*4*0=0, where the sequence ends.
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8$\begingroup$ One way to look at it is that the sequence ends. Another way is that it goes on forever, in an incredibly boring manner. $\endgroup$ Commented Feb 18, 2015 at 1:08
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$\begingroup$ @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 BronCommented Feb 18, 2015 at 1:21
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$\begingroup$ It will be interesting if the distribution of getting to a certain value from a starting number will be different than 10% $\endgroup$– MotiCommented Feb 18, 2015 at 5:59
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$\begingroup$ 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. $\endgroup$ Commented Apr 20, 2016 at 15:05
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$\begingroup$ @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. $\endgroup$ Commented Aug 29, 2016 at 14:41