# Math sequence puzzle

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

• Hard to say, can you also tell me the expiration date and the three numbers on the back? – user2023861 Sep 23 '15 at 19:26
• This isn't very much information. It seems like you're getting the numbers from somewhere else. Can you provide more context? – Engineer Toast Sep 23 '15 at 19:30
• Should we be looking for an answer that COMPLETES the sequence or CONTINUES it? – Gordon K Sep 23 '15 at 19:30
• See also here: itstoohard.com/puzzle/2pXK7kIq – Sleafar Sep 23 '15 at 19:32
• 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 $f(6)=106238$. – Rohcana Sep 23 '15 at 19:41

## 1 Answer

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