What is the formula for these pattern data sequences?

In summary, there is no clear formula that can be derived for the given series of numbers. While there are ways to fit the points to a curve, the meaning and significance of these formulae are questionable due to the potential use of arbitrary constants. Additionally, the numbers do not represent anything in particular and do not yield any meaningful results when inputted into certain mathematical operations.
  • #1
ryan8200
7
0
How to derive formula for the series of numbers as below:
(a) 4,8,15,16,23,42
(b) 4,17, 23,38,41,46
 
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  • #2
The sequences are so jerky that you really need longer samples for the question even to be meaningful. Yes, you could make up formulae to generate these, but they would likely contain five or more arbitrary constants, so you'd have no confidence they mean anything.
 
  • #3
Hi Ryan. Do the numbers represent anything in particular? Do you have a reason to use such a formula, like interpolation or extrapolation?

There are many ways to fit those points to a curve, but whether or not any particular formula has any significant meaning is another question.

For the first one for example, you can write:

[tex]T_k = - \frac{9}{40} k^5 + \frac{25}{8} k^4 - \frac{117}{8} k^3 + \frac{215}{8} k^2 - \frac{223}{20} k + 4 \, \, \, \, \, : \,k = 0,1,2,3 \ldots[/tex]
 
  • #5
Another series for the first one is,

[tex] T_k = \frac{1}{217} \left( 454 \, T_{k-3} - 63 \, T_{k-2} + 144 \, T_{k-1} \right) [/tex]
 

What is a formula for pattern data?

A formula for pattern data is a mathematical equation or algorithm that is used to identify and describe patterns in a set of data. It allows scientists to make predictions and draw conclusions based on the observed patterns.

How is a formula for pattern data created?

A formula for pattern data is typically created by analyzing a set of data and identifying any recurring patterns. Scientists may use various techniques such as regression analysis, Fourier analysis, or machine learning algorithms to develop a formula that accurately describes the patterns in the data.

Why is a formula for pattern data important?

A formula for pattern data is important because it allows scientists to make sense of complex data and understand the underlying relationships and trends within it. It also enables them to make predictions and identify potential patterns in future data.

Can a formula for pattern data be applied to any type of data?

Yes, a formula for pattern data can be applied to various types of data, including numerical, categorical, and even qualitative data. However, the type of formula and method used to analyze the data may vary depending on the type of data being studied.

What are some common challenges in creating a formula for pattern data?

Some common challenges in creating a formula for pattern data include identifying the appropriate variables and factors to include in the formula, dealing with missing or incomplete data, and choosing the most suitable statistical analysis method for the data set.

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