- #1
joeyar
- 53
- 0
2, 8, 62, 622, 7772, ...
What is the next number in the sequence?
- Thread starter joeyar
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In summary, I think everyone should just agree to call 17 the next number in these sequences, because it seems like it would make life a lot easier.
- #2
daskalou
- 9
- 0
116584?
- #3
Jimmy Snyder
- 1,127
- 21
I get
117644
n^(n-1) - n + 2
eom
117644
n^(n-1) - n + 2
eom
- #4
daskalou
- 9
- 0
jimmysnyder said:
Ahh, good work, you're right.
- #5
joeyar
- 53
- 0
Yes, jimmysnyder got it. Well done mate.
- #6
RandallB
- 1,550
- 0
And quick too,jimmysnyder said:
did you use any "special logic” to guide your judgment to a solution
or was it random attempts and personal "feel".
- #7
Jame
- 42
- 0
Got it too, love these brain teasers!
I first noticed there was exponential growth involved, I tried dividing the terms and noticed that the quotient of a term and its predecessor was increasing. I then did som algebra and noticed that expressions of the form n^A has a quotient approaching 1 as n approaches infinity, which doesn't fit this case. I then tried n^n and found that it met the increasing-quotient criteria, but the actual numbers for the cases of n = 1, 2, 3, 4 .. were a bit off. I then realized that it had to be n^(n-1) which gave me an almost perfect fit, except for a linearly increasing difference. This last term turned out to be (-n + 2). The next number therefore has to be n^(n-1) - n + 2 = 7^6 - 7 + 2 = 117644
When I do these kinds of puzzles I like to forget my knowledge of calculus and series and just do it the way I did when I was smaller and there was an exciting number-quiz in the newpaper. :)
I first noticed there was exponential growth involved, I tried dividing the terms and noticed that the quotient of a term and its predecessor was increasing. I then did som algebra and noticed that expressions of the form n^A has a quotient approaching 1 as n approaches infinity, which doesn't fit this case. I then tried n^n and found that it met the increasing-quotient criteria, but the actual numbers for the cases of n = 1, 2, 3, 4 .. were a bit off. I then realized that it had to be n^(n-1) which gave me an almost perfect fit, except for a linearly increasing difference. This last term turned out to be (-n + 2). The next number therefore has to be n^(n-1) - n + 2 = 7^6 - 7 + 2 = 117644
When I do these kinds of puzzles I like to forget my knowledge of calculus and series and just do it the way I did when I was smaller and there was an exciting number-quiz in the newpaper. :)
- #8
Borek
Mentor
- 29,023
- 4,366
11111. These are roots of the following polynomial:
[tex]f(x) = x^6-19577x^5+99504914x^4-60788218692x^3+3929719423336x^2-34258540436320x+53282917476608[/tex]
[tex]f(x) = x^6-19577x^5+99504914x^4-60788218692x^3+3929719423336x^2-34258540436320x+53282917476608[/tex]
- #9
Jame
- 42
- 0
Ah, how could I have missed something so obvious!
- #10
Jimmy Snyder
- 1,127
- 21
The fact that 8, 62, and 622 are all close to small powers of small integers, and off by 1, 2, and 3 was the key for me.RandallB said:
- #11
Jimmy Snyder
- 1,127
- 21
That's quite a coincidence. It turns out that 11111 is also the next number in the sequence:Borek said:
1 -19577 99504914 -60788218692 3929719423336 -34258540436320 53282917476608
- #12
Borek
Mentor
- 29,023
- 4,366
TBH that's not my idea. I believe originally it was claimed that 17 is the next number in every sequence, but I don't remember who was the author.
- #13
YesIam
- 42
- 0
Hi Borek and others - I just happened on this forum a couple of days ago. Maybe you all are way ahead of me...or maybe not. I thought it was common knowledge that any number can be a correct number in a series sequence like these. Almost like Borek says, except, "...17 can be...", rather than, "...17 is..." I think that can be chiseled in stone.
FAQ: What is the next number in the sequence?
1. What is the pattern of the sequence?
The first step in determining the next number in a sequence is to identify the pattern. This could be a simple arithmetic progression, where each number increases or decreases by a fixed amount, or it could be a more complex pattern involving multiplication, division, or other operations.
2. Are there any missing numbers in the sequence?
If there are missing numbers in the sequence, it could indicate a more complex pattern or a mistake in the sequence itself. It's important to check for missing numbers and determine if they fit into the pattern or not.
3. Can the sequence be extended infinitely?
Some sequences have a clear pattern and can be extended infinitely, while others may have a limited number of terms before the pattern breaks down. It's important to analyze the sequence and determine if it can be extended indefinitely or not.
4. Are there any outliers in the sequence?
Outliers are numbers that do not fit the established pattern of the sequence. It's important to identify and analyze outliers to determine if they are significant and if they should be included in determining the next number in the sequence.
5. How confident are you in the predicted next number?
Predicting the next number in a sequence is not an exact science and there is always a margin of error. It's important to be aware of this and to consider the complexity of the pattern and the presence of outliers when determining the confidence level of the predicted next number.