[frosstykiss]

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.

[ebaines]

6512

[Washington1]

I agree: 6512

[eeseely]

How about showing you logic for the solution.

[morgaine300]

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 )

[KISS]

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

[Unknown008]

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

[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.

[Capuchin]

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.

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

[ebaines]

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

True enough!

[eeseely]

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

[morgaine300]

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.)

[Unknown008]

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:

[ebaines]

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.

[Capuchin]

I have an inherent dislike for non infinite sequences ;)

[Unknown008]

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

[ebaines]

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

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

[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:

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

[chancelord]

I believe they are right it must be 6512