- #1

jframe

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2 6 9 23 17 36 22 24 26 32 41 43 ?

what is the next number in the above sequence?

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In summary, there are an infinite number of sequences that can have 42 as all members, and finding a formula to determine the next number in a sequence is possible but can be complex. Patterns and randomness are mutually exclusive, so if the numbers are truly random, there will be no pattern to determine the next number. In order to find the simplest formula, the environment and measure of complexity must be defined, and it may take exponential time to discover the shortest formula.

- #1

jframe

- 5

- 0

2 6 9 23 17 36 22 24 26 32 41 43 ?

what is the next number in the above sequence?

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- #2

CRGreathouse

Science Advisor

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jframe said:what is the next number in the above sequence?

42. There are an infinite number of sequences that, apart from some finite chunk at the beginning, have 42 as all members.

- #3

qntty

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- #4

jframe

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- #5

qntty

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- #6

jframe

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i'd like to find a formula i can use that outputs these numbers, so that i can figure out what the next number is

for example, if i randomly chose the numbers 2 4 6 8 10 12 14 16 18 20 22 24, i could use the formula n*2

is there a formula i can use for 2 6 9 23 17 36 22 24 26 32 41 43?

- #7

qntty

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- #8

CRGreathouse

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jframe said:is there a formula i can use for 2 6 9 23 17 36 22 24 26 32 41 43?

Sure, the one I suggested above can be coded in Pari as

Code:

`jframe(n)=if(n<1,0,[2,6,9,23,17,36,22,24,26,32,41,43,42][min(n,13)])`

Also, there's an 11th-degree polynomial that fits those points exactly.

- #9

jframe

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for example, if i randomly chose 1 2 3 4 5 6 7 8 9 10 11 12, i could come up with a less complex formula than an 11th-degree polynomial

i have a feeling the answer to my original question is no. thanks for the help, though

- #10

qntty

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- #11

CRGreathouse

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jframe said:is there any way to simplify it and get a less complex formula?

for example, if i randomly chose 1 2 3 4 5 6 7 8 9 10 11 12, i could come up with a less complex formula than an 11th-degree polynomial

Ah. Now you're getting into the interesting realm of Kolmogorov complexity.

In general, you won't be able to find a way to get a less complex formula to describe your data than the data itself. For some sequences it is possible. The troubles:

- You must define the environment in which complexity is to be measured (e.g., Pari programs, or closed-form RPN formulas using the following characters: "012n+-*/^!") and the measure of complexity (e.g. characters).
- Discovering the shortest formula takes exponential time.

- #12

DaleSwanson

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- #13

jframe

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i'm not picking a random 13th number, dale. I'm looking for the simplest pattern/formula i can find in the randomly chosen 12 numbers to determine the 13th number. if I'm lucky enough to pick 1 2 3 4 5 6 7 8 9 10 11 12, then the simplest formula i can find is f(n)=n

Finding the next number in a sequence of randomly chosen numbers is a task often used in statistics and data analysis. It can help identify patterns or trends in the data and make predictions about future values.

The next number in a sequence of randomly chosen numbers can be determined by looking for patterns or relationships between the numbers. This can include identifying a mathematical rule or using statistical techniques such as regression analysis.

No, it is not possible to predict the next number in a sequence of randomly chosen numbers with 100% accuracy. This is because randomness inherently includes an element of unpredictability.

Some common strategies for finding the next number in a sequence of randomly chosen numbers include using mathematical formulas, analyzing the data for patterns, and using machine learning algorithms.

The accuracy of predicting the next number in a sequence of randomly chosen numbers is measured by comparing the predicted value to the actual value. This can be done using statistical measures such as mean absolute error or root mean squared error.

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