What is the equation for this pattern? (x=0, 2, 4, 16, 256, 65536)

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

Discussion Overview

The discussion revolves around finding an equation that generates a specific numerical pattern: 2, 4, 16, 256, 65536. Participants explore various mathematical approaches to derive a formula that aligns with the given values based on the input variable x.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that the pattern can be expressed as powers of 2: 2^1, 2^2, 2^4, 2^8, 2^16.
  • Another participant proposes the function f(x) = 2^(2x) but later finds that it does not yield the correct sequence.
  • A later reply indicates that the correct formula is 2^(2^x), but notes that substituting x=1 does not produce the first number in the sequence, suggesting that x=0 should be used instead.
  • One participant expresses concern about providing explicit formulas, initially assuming the inquiry was for homework, but later clarifies it is for a programming project.
  • There is a correction regarding the initial misunderstanding of the input value for x, emphasizing that x=0 should be the starting point for the equation to match the pattern correctly.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formula initially, with multiple proposed equations and corrections made throughout the discussion. The final suggestion of 2^(2^x) is acknowledged, but there remains uncertainty about the appropriate input value for x.

Contextual Notes

There are limitations regarding the assumptions made about the input values for x and how they relate to the output sequence. The discussion highlights the need for clarity in defining the starting point for the equation.

Qwerty
I have the following pattern and i need an equation that if x = 1 then y will equal the fist number of it, if x = 2, then y will equal the 2nd number.

The pattern is:
2, 4, 16, 256, 65536

Hint: It keeps squaring itself.

Any ideas?
 
Mathematics news on Phys.org
Try writing all of them as powers of 2:
21,22,24,28,216

It should be easy from there...
 
Try writing all of them as powers of 2
But this doesn't help me much becasue it doesn't find my numbers i need in an equation...
 
f(x) = 2^2x
 
Last edited:
f(x) = 2^2x
I had already thought of this but it does not work...Here is the pattern it gives you.
4,16,64,256
This is the pattern I want...
2, 4, 16, 256, 65536

There is not supposed to be 64 and it also skips 2
 
it turns out to be quite a function with an even nicer derivative
 
I don't think we should be giving explicit formulas anyway, since it sounds like homework.
Acually no, it's not for homework...its for a project I am working on(programming).

And I don't need your help anymore, I found the answer to my question myself.
Answer: 2^(2^x)
 
Originally posted by Qwerty
Acually no, it's not for homework...its for a project I am working on(programming).

And I don't need your help anymore, I found the answer to my question myself.
Answer: 2^(2^x)
Originally posted by Qwerty
I have the following pattern and i need an equation that if x = 1 then y will equal the fist number of it, if x = 2, then y will equal the 2nd number.

The pattern is:
2, 4, 16, 256, 65536

Hint: It keeps squaring itself.

Any ideas?
if you first put x=1 (as you requested) to this equation you get 2^(2^1)=4 which is not the first number 2 ofcourse.
but if you put first x=0 then this is the equation you were looking for this pattern.
 
if you first put x=1 (as you requested) to this equation you get 2^(2^1)=4 which is not the first number 2 ofcourse.
Yes this is an error in my first post, 0 is supposed to be the first number subsituted into the equation.
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
2
Views
2K
Replies
10
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 68 ·
3
Replies
68
Views
13K
  • · Replies 8 ·
Replies
8
Views
3K