What Comes Next in This Finite Sequence?

  • Context: Undergrad 
  • Thread starter Thread starter micromass
  • Start date Start date
Click For Summary

Discussion Overview

The thread discusses a finite sequence of numbers and seeks to identify the next number in the sequence. Participants explore the underlying patterns and mathematical theories related to the sequence, particularly focusing on the behavior of exponents and connections to group theory.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents a sequence of numbers and expresses doubt about its indefinite extension.
  • Another participant guesses that the next number in the sequence is 71 and proposes a relationship involving powers of prime numbers.
  • A subsequent reply confirms that 71 is indeed correct and invites others to explore the reasoning behind the behavior of the exponents, hinting at the theory of simple groups.
  • One participant suggests that the order of the monster group may be relevant to understanding the exponents, indicating familiarity with the topic.
  • A later reply expresses a light-hearted admission of having "cheated" in their understanding of the sequence.

Areas of Agreement / Disagreement

Participants generally agree on the next number being 71, but the reasoning behind the behavior of the exponents remains open for exploration and discussion, with no consensus reached on the explanation.

Contextual Notes

The discussion includes references to advanced mathematical concepts, such as the theory of simple groups and the monster group, which may not be accessible to all participants. The reasoning behind the exponents is not fully resolved, leaving room for further inquiry.

Who May Find This Useful

Individuals interested in number theory, group theory, and mathematical sequences may find this discussion relevant and engaging.

micromass
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Messages
22,170
Reaction score
3,333
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...)
 
Mathematics news on Phys.org
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...
 
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
 
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. :(
 
Sorry :blushing:

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

Similar threads

Graduate About a natural extension of Collatz conjecture
  • · Replies 3 ·
Replies
3
Views
1K
MCNP Tally f8 unreliable since neutron transport is nonanalog
  • · Replies 3 ·
Replies
3
Views
4K
How to calculate dark count from data collected?
  • · Replies 11 ·
Replies
11
Views
3K
Can You Decode This List of Numbers into a Message?
  • · Replies 18 ·
Replies
18
Views
15K
Undergrad Can This Formula Identify All Prime Numbers?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Godel Escher Bach: Interesting number sequence
  • · Replies 3 ·
Replies
3
Views
5K
Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
  • · Replies 2 ·
Replies
2
Views
1K
Minimum # of ops to even out an array by....
  • · Replies 9 ·
Replies
9
Views
2K
Comp Sci Counting Numbers in Curly Braces in Fortran?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Equation for number placement in Sudoku-like grid
  • · Replies 10 ·
Replies
10
Views
6K