What is the next number in this sequence?
1
721
727
5767
5791
5792

Been trying but seem to not quite get the answer

What I come out with seems to far out.
I know there is ways to use comp program but not sure how to
Get it set up LOl
Usually do these in my head but this time its not working.

6512

I agree: 6512

How about showing you logic for the solution.

Yes, can you please show how you solved this. Even with the answer I could not figure this out and would be curious what you did. (Somehow I have a feeling this is into something over my head. :p )

Now that I see the pattern after your solution, I think the next number after 6512 is 6518.

Can one of you three (ebaines, washington1 or keepitsimplestupid) tell why these are the next numbers in that pattern?

OK:

1 = 1!
721 = 1! +6!
727 = 1! + 6! + 3!
5767 = 1! + 6! + 3! + 7!
5791 = 1! + 6! + 3! + 7! + 4!
5792 = 1! + 6! + 3! + 7! + 4! + 1!

So the real question is: what's the pattern in 1, 6, 3, 7, 4, 1,.

It seems that there's a pattern based around the 7, which is the center term in a sequence of 7 numbers - note that 7 = 3+4 and also 7 = 6+1. So the next number in the sequence is a 6, as 1+6 = 7. Adding 6! To 5792 gives 6512. At this point the sequence is ended.

Quote:

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Originally Posted by ebaines

OK:

1 = 1!
721 = 1! +6!
727 = 1! + 6! + 3!
5767 = 1! + 6! + 3! + 7!
5791 = 1! + 6! + 3! + 7! + 4!
5792 = 1! + 6! + 3! + 7! + 4! + 1!

So the real question is: what's the pattern in 1, 6, 3, 7, 4, 1, ...

It seems that there's a pattern based around the 7, which is the center term in a sequence of 7 numbers - note that 7 = 3+4 and also 7 = 6+1. So the next number in the sequence is a 6, as 1+6 = 7. Adding 6! to 5792 gives 6512. At this point the sequence is ended.

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Of course, either of those 1!s could be 0!s, so perhaps the next term could be either +6! Or +7!

Quote:

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Originally Posted by Capuchin

Of course, either of those 1!s could be 0!s, so perhaps the next term could be either +6! or +7!

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True enough!

I see said the sight impaired man as he picked up his hammer and saw!

Well... I can only say it would've never occurred to me in a million years it was the sum of a bunch of factorials! (Pardoning the pun.)

Wow, finally. Kind of... amazing! :rolleyes:

But after +7! has the sequence ended? Because... I can't find the other possible numbers to be added to have 7 (following the pattern of 0! + 1! + 6! + 3! + 7! + 4! + 1! + 6! + 7!)
:confused:

The sequence ends with 7 terms - as it is based on the symmetry of the sums on either side of the 4th term. So the sequence is either:

1! + 6! + 3! + 7! + 4! + 1! + 6!
Or
0! + 6! + 3! + 7! + 4! + 1! + 7!


That's it.

I have an inherent dislike for non infinite sequences ;)

Ah, then I was right when I said that the sequence ends with 7! or like you mentioned 6!

Quote:

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Originally Posted by Unknown008

Ah, then i was right when I said that the sequence ends with 7!, or like you mentioned 6!.

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Well yes, it can end with a 6! or a 7! but it doesn't end with 6! + 7!

Quote:

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Originally Posted by Unknown008

Wow, finally. Kinda... amazing! :rolleyes:

But after +7! , has the sequence ended? cauz... i can't find the other possible numbers to be added to have 7 (following the pattern of 0! + 1! + 6! + 3! + 7! + 4! + 1! + 6! + 7!)
:confused:

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Oh yeah, I forgot to mention my error I made earlier. I've forgotten that 0! Is also 1:o

I believe they are right it must be 6512