what number is next

[Dai]

what number is next in the sequence 2, 4, 7, 13, 715, 62347, ?

 

[HallsofIvy]

You understand, I imagine, that there is NO one answer to a question like this. A sequence can start in any way you like, then add on whatever numbers you want. What you are really asking is "is there a simple rule that will give these numbers". I certainly don't see one! Is there more information about this sequence that might help?

 

[Dai]

I do understand that, thought that it is logical that i was wondering for the rule that can be apply for the sequence
And i don't really know what is the rule that can be apply for that sequence ... i can see the rule for the first 4 numbers, but that kind of progression with last two digits is unknown to me, so i asked for help

 

[Dai]

2+4+1=7
4+7+2=13
so the 4th should be
7+13+3= 23 but it is 3digits number instead

also it looks like some variation of tribonacci sequence but again, it can not be applied for the 4th and 5th number, hence the ask for help

 

[Ishuda]

Whatever...the jump from 13 to 715 is enough to make this some kind of joke...

There are sequences which grow extremely quick. For one of the 'smaller' ones you have the tower function
a_i,1 = i
a_i,j = \(\displaystyle i^{a_i,_{j-1}}\)
The tower is
t_j = a_j,j
so we have for t_j
1, 2²=4, \(\displaystyle 3^{3^3}=7625597484987\), ...
and that 4th term - well let's just say that it is large.