-3
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Complete the sequence:

5928 1411 9909 1882 5419 ...

It doesn't seem like a simple polynomial fit will work, I have tried the difference method and the quotient method. Any hint would be appreciated. Thanks

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5
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    $\begingroup$ Hard to say, can you also tell me the expiration date and the three numbers on the back? $\endgroup$ Sep 23, 2015 at 19:26
  • $\begingroup$ This isn't very much information. It seems like you're getting the numbers from somewhere else. Can you provide more context? $\endgroup$ Sep 23, 2015 at 19:30
  • $\begingroup$ Should we be looking for an answer that COMPLETES the sequence or CONTINUES it? $\endgroup$
    – Gordon K
    Sep 23, 2015 at 19:30
  • $\begingroup$ See also here: itstoohard.com/puzzle/2pXK7kIq $\endgroup$
    – Sleafar
    Sep 23, 2015 at 19:32
  • $\begingroup$ Polynomial fitting generates the polynomial $f(x) = $ $$2401.20833...x⁴ - 28935.4166...x³ + 120089.79166...x² - 198256.5833...x + 110629$$ which gives the next term $f(6)=106238$. $\endgroup$
    – Rohcana
    Sep 23, 2015 at 19:41

1 Answer 1

12
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The next number in this sequence is:

3655 (confirmed at the link provided by Sleafar)

This sequence is based on the:

Middle-square method for generating pseudorandom numbers.

In this case, the sequence starts with a 4 digit seed (5928), which is then squared (35141184). The middle 4 digits of the result become the next number in the sequence. If the result is less than 8 digits, leading zeroes are provided.

So, this sequence progresses as:

5928  35141184
1411  01990921
9909  98188281
1882  03541924
5419  29365561
3655  13359025
3590  12888100

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