- #1
holomorphic
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What's the next number?
1, 1, 6561, 2197, 289, 21, 1, 707281, ...?
1, 1, 6561, 2197, 289, 21, 1, 707281, ...?
What's the Pattern in This Number Sequence?
- Thread starter holomorphic
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In summary, to determine the next number in a sequence, it is important to identify the pattern of the given numbers. This can involve using arithmetic or geometric sequences, or other mathematical patterns. While there may be a specific rule or formula for finding the next number in some cases, there can also be multiple patterns that can result in different next numbers. The accuracy of predicting the next number depends on the complexity and consistency of the pattern, and there may be limitations to predicting the next number if the sequence is more complex or appears random.
- #2
tiny-tim
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hmm …
well, that's 1, 1, 94, 133, 172, 211, 250, 294 …
i don't see where the 1 at the start fits in
well, that's 1, 1, 94, 133, 172, 211, 250, 294 …
i don't see where the 1 at the start fits in
- #3
arildno
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tiny-tim said:hmm …
well, that's 1, 1, 94, 133, 172, 211, 250, 294 …
i don't see where the 1 at the start fits in
Well, that would be:
[tex]1^{...}, 5^{0},9^{4},13^{3}, 17^{2}, 21^{1}, 25^{0}, 29^{4}[/tex]
So, the next would be [itex]33^{3}[/itex], whatever the exponent of the first number in the sequence.
- #4
tiny-tim
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oh, i get it now! … it starts 11, 50
- #5
holomorphic
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arildno said:
Yup :)
FYI, the exponents are the bases mod 5.
So the formula for the kth term is:
[tex](4k+1)^{4k+1 MOD 5}[/tex]
FAQ: What's the Pattern in This Number Sequence?
What is the pattern of the numbers?
To determine the next number, we need to identify the pattern of the given numbers. This can include arithmetic sequences, geometric sequences, or other mathematical patterns.
Is there a specific rule or formula for finding the next number?
In some cases, there may be a specific rule or formula that can be used to find the next number. This could involve adding or subtracting a certain number, multiplying or dividing by a certain number, or using a combination of operations.
Can different patterns result in different next numbers?
Yes, depending on the complexity of the sequence, there may be multiple patterns that can be used to determine the next number. It is important to carefully analyze the given numbers to determine the most appropriate pattern to use.
How accurate is the prediction of the next number?
The accuracy of predicting the next number depends on the complexity and consistency of the pattern. If the pattern is simple and consistent, the prediction will likely be accurate. However, if the pattern is more complex or irregular, the prediction may be less accurate.
Are there limitations to predicting the next number?
Yes, there are limitations to predicting the next number. It is important to note that not all number sequences follow a pattern, and some may even appear random. In these cases, it may not be possible to accurately predict the next number.