Next (2) what is the next number?

  • Context: High School 
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Discussion Overview

The discussion revolves around identifying the next number in a sequence of integers: 4, 9, 25, 49, 22, 52, 136, 19, and potentially the next two terms. The conversation includes various hypotheses and guesses regarding the underlying pattern or rule governing the sequence.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that each term has a concurrent prime factor, providing examples of how the numbers relate to prime factorization.
  • Another participant suggests a guess of 69 as the next number, indicating uncertainty in the pattern.
  • A later reply proposes that the next number could be 5*23, linking the last factors to primes and the first factors to primes modulo 9.
  • There is a challenge regarding the classification of 4 and 8 as prime, with participants clarifying that they are not prime but relate to primes modulo 9.
  • One participant lists several numbers (115, 58, 124, 37, 205, and 301) as potential next terms, but it is unclear how these relate to the previous numbers.

Areas of Agreement / Disagreement

Participants express differing views on the next number in the sequence, with multiple guesses and interpretations of the pattern. No consensus is reached regarding the correct next term or the underlying rule.

Contextual Notes

Some assumptions about the sequence's structure and the definitions of prime factors are not fully resolved, leading to uncertainty in the proposed patterns.

holomorphic
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What is the next number?

4, 9, 25, 49, 22, 52, 136, 19, ...?

EDIT: bonus, find the next TWO terms. With a few random guesses you could find the next term at this point.
 
Last edited:
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I found that each term has the concurrent prime factor.

4 = 2*2

9 = 3*3

25 = 5*5

49 = 7*7

22 = 2*11

52 = 4*13

136 = 8*17

19 = 1* 19

I don't know what to say about the other factors.
 
Is the next number 69? Just a guess...
 
micromass said:
Is the next number 69? Just a guess...

No, but you could probably make a few more guesses like that and get it.

Even if that's cheap =P
 
Ah, then it must be 5*23.

The last factors are all the primes, and the first factors are the primes modulo 9...

Is that correct?
 
How is 4 or 8 prime?
 
micromass said:
Ah, then it must be 5*23.

The last factors are all the primes, and the first factors are the primes modulo 9...

Is that correct?

Yep yep yep. A.
 
115 and 58 are the next two followed by 124, 37, 205, and 301.
 
Dickfore said:
How is 4 or 8 prime?

They aren't. But 4 = 13 MOD 9, and 8 = 17 MOD 9.
 
  • #10
holomorphic said:
They aren't. But 4 = 13 MOD 9, and 8 = 17 MOD 9.

Ah, I see.
 
  • #13
holomorphic said:
Who double posted?

I did.
 

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