What Comes Next in This Finite Sequence?

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In summary, the conversation involved a finite sequence of numbers and the challenge of finding the next number in the sequence. The conversation also mentioned the theory of simple groups and the order of the monster group. The next numbers in the sequence are determined by the order of the monster group.
  • #1
micromass
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I'd be extremely impressed if anybody finds this one:

70 368 744 177 664, 3 486 784 401, 1 953 125, 117 649, 121, 2197, 17, 19, 23, 29, 31, 41, 47, 59


This is a finite sequence. It can not be extended indefinitely (to my knowledge...)
 
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  • #2
micromass said:
I'd be extremely impressed if anybody finds this one:

70 368 744 177 664, 3 486 784 401, 1 953 125, 117 649, 121, 2197, 17, 19, 23, 29, 31, 41, 47, 59


This is a finite sequence. It can not be extended indefinitely (to my knowledge...)

Uhh... 71? (Guess.)

[tex]2^{46}, 3^{20}, 5^{9}, 7^{6}, 11^{2}, 13^{3}, ... [/tex]
Then the ones that follow are to the first power. I don't know why the exponents would go 1,1,1,3,2,6,9,20,46...
 
  • #3
Yes, 71 is correct. I didn't expect somebody to find this that quick... :smile:
Is there anybody that can figure out why the exponents behave this way. Hint: theory of simple groups
 
  • #4
micromass said:
Yes, 71 is correct. I didn't expect somebody to find this that quick... :smile:
Is there anybody that can figure out why the exponents behave this way. Hint: theory of simple groups

Oh... order of the monster group. Pblackffffft. Because I use that every day.

Note: I cheated. :(
 
  • #5
Sorry :blushing:

I really like the monster group :biggrin: I'll keep the next ones more down-to-earth...
 

1. How does "Guess the next number" work?

"Guess the next number" is a game where the player is given a sequence of numbers and has to guess the next number in the sequence. The sequence can follow any pattern, such as increasing or decreasing by a certain amount, or following a mathematical rule.

2. Can anyone win at "Guess the next number"?

Yes, anyone can win at "Guess the next number" if they are able to identify the pattern or rule behind the sequence of numbers and make an accurate guess for the next number.

3. Is there a specific strategy to increase my chances of winning at "Guess the next number"?

There is no guaranteed strategy for winning at "Guess the next number" as the sequence of numbers can follow any pattern. However, paying attention to the previous numbers and trying to identify any patterns or rules can increase your chances of making an accurate guess.

4. Is there a limit to how many numbers can be in the sequence for "Guess the next number"?

No, there is no limit to how many numbers can be in the sequence for "Guess the next number". The sequence can be as short or long as desired, as long as there is a clear pattern or rule behind it.

5. Can "Guess the next number" be used for educational purposes?

Yes, "Guess the next number" can be used for educational purposes to help students develop their critical thinking and problem-solving skills. It can also be used to introduce mathematical concepts such as patterns and sequences in a fun and engaging way.

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