Number sequence

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Michael606

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Aug 22, 2022
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A friend of mine gave me a sequence, but I don't find out the pattern(s)/rule(s). Maybe you can help?

8, 12, 18, 24, 38, 60, 98, 150, 240, 380, 614,
 
Michael606 said:
A friend of mine gave me a sequence, but I don't find out the pattern(s)/rule(s). Maybe you can help?

8, 12, 18, 24, 38, 60, 98, 150, 240, 380, 614,
Click to expand...
Please advise your friend to communicate directly with us. That way we can teach your friend - the procedure to solve these problems - a lot more efficiently.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Michael606 said:
A friend of mine gave me a sequence, but I don't find out the pattern(s)/rule(s). Maybe you can help?

8, 12, 18, 24, 38, 60, 98, 150, 240, 380, 614,
Click to expand...
Unless you happen to stumble upon the solution you aren't going to get anywhere. There are even series that have more than one solution, given the starting numbers. Without knowing more about what your friend is thinking it is pretty much impossible to do this. There is no general method for solving these because I can pick any number for the next one and make it work with the right fit.

-Dan
 
Okay, I hoped, here were some "math gifted" people who have a "sense" for such things. Of course I googled first and tried common rules, but I don't have a "feeling" for this.
 
Michael606 said:
A friend of mine gave me a sequence, but I don't find out the pattern(s)/rule(s). Maybe you can help?

8, 12, 18, 24, 38, 60, 98, 150, 240, 380, 614,
Click to expand...
Is there any context, or was this just given as a puzzle? Tell us more about it.

This is not a polynomial, or any other standard sequence I can see; in general, you can never be sure what rule, if any, was used to make a given finite sequence. If it were anything well-known, or nearly so, it would be found here:

Michael606 said:
Okay, I hoped, here were some "math gifted" people who have a "sense" for such things. Of course I googled first and tried common rules, but I don't have a "feeling" for this.
Click to expand...
This isn't really math, unless the numbers come from some context other than your friend's mind. It's a guessing game.
 
Michael606 said:
Any other ideas?
Click to expand...
We've given you all the time this is worth. You haven't answered our questions; why should we do any more for you?

To repeat, questions like this are just riddles, often equivalent to "What have I got in my pocket?". One might guess how someone obtained the numbers, but that wouldn't even be evidence that that is the intended answer. So it is not worth spending any time on.
 
The following is almost certainly not what your friend is looking for. However, it works exactly (for n=0,1,2,...,9,10)

[math]\dfrac{109}{453600}n^{10} - \dfrac{179}{15120}n^9 + \dfrac{1511}{6048}n^8 - \dfrac{62}{21}n^7 + \dfrac{462907}{21600}n^6 - \dfrac{14189}{144}n^5 + \dfrac{5169443}{18144}n^4 - \dfrac{186853}{378}n^3 + \dfrac{5801129}{12600}n^2 - \dfrac{17554}{105}n + 8[/math]
In plain text: 109/453600*n^10 - 179/15120*n^9 + 1511/6048*n^8 - 62/21*n^7 + 462907/21600*n^6 - 14189/144*n^5 + 5169443/18144*n^4 - 186853/378*n^3 + 5801129/12600*n^2 - 17554/105*n + 8

There are infinite expressions that would generate your friend's sequence. It's pretty difficult to find each one. Therefore finding a "simple/ elegant/ neat" expression would be extremely difficult. Puzzles are meant to be challenging but possible to solve within a reasonable time frame. Therefore, in my opinion, and with the best intent, your friend has failed to give you a "nice/ fun" puzzle to do. It's just too hard without extra clues/ info :)

EDIT: If you want the next number to be "x" then use this beauty: x/39916800*n^11 - 739/9979200*n^11 - x/725760*n^10 + 559/129600*n^10 + x/30240*n^9 - 1657/15120*n^9 - 11/24192*x*n^8 + 1205/756*n^8 + 683/172800*x*n^7 - 4425959/302400*n^7 - 781/34560*x*n^6 + 3811609/43200*n^6 + 31063/362880*x*n^5 - 31894627/90720*n^5 - 7645/36288*x*n^4 + 2352679/2592*n^4 + 16103/50400*x*n^3 - 54385651/37800*n^3 - 671/2520*x*n^2 + 1746501/1400*n^2 + x/11*n - 503474/1155*n + 8
 
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I'm wondering whether the friend's motivation is to cheat at some game…

[imath]\;[/imath]
 
My friend gave me more numbers, so the sequence is now:

8, 12, 18, 24, 38, 60, 98, 150, 240, 380, 614, 992, 1602, 2592, 4202, 6780, 10950,

It's quite obvious, that one rule is to add two numbers to get the next one; e.g. 8+12=20, but the number in the sequence is always a little bit lower. So there has to be a second rule for this. Maybe one of you can find it
 
It's quite obvious, that one rule is to add two numbers to get the next one.
How can it be an obvious rule if it does not work??

In post #7, you were given a rule that works! Did you even try to see if it works?!
The formula is: f(n) =109/453600*n^10 - 179/15120*n^9 + 1511/6048*n^8 - 62/21*n^7 + 462907/21600*n^6 - 14189/144*n^5 + 5169443/18144*n^4 - 186853/378*n^3 + 5801129/12600*n^2 - 17554/105*n + 8

Did you notice that f(0) = 8?
How about f(1) =12?
Maybe that f(2) = 18?
Would you believe that f(3)=24?

This is a formula that works! Isn't that what you were looking for?
 
You have been told that this is not math. Why?

Because there are an infinite number of formulas that will generate this sequence. In fact, there are an infinite number of polynomials that will generate this sequence. So asking what is “the” answer is asking a question that has no answer.

You were given a link to sequences that have some mathematical interest.
 
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