Discovering formula for a sequence with recurring digits

It seems to be a nested formula regrouping we get: (1,2),(1,2,3,4),(1,2,3,4,5,6),(1,2,3,4,5,6,7,8),...

 

I don't understand how you would continue this sequence as 10,11,12,... are not digits. This makes it improvable that you have a sequence of recurring digits.

 

There is either not enough information or the process repeats modulo 10.

 

Why does it matter that they are not digits? why can't you have:

......1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,5,6,7,8,9,10,11,12,13,14.......

for example? If you really need a sequence of digits rather than numbers you can just take out the commas:

......1234567891011121234567891011121314.......

 

OEIS is the answer to all these kinds of questions.

http://oeis.org/search?q=1,2,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,7,8&language=english&go=Search

 

I was confused by the title in which the op called it a sequence with recurring digits rather than a sequence of numbers. It is not a sequence of digits because the 30th term is 10 which is not a digit.

 

[itex]\left\{\left\{k\right\}^{2n}_{k=1}\right\}^{∞}_{n=1}[/itex]

My lack of LaTex knowledge may make this awful, but the idea is a nested sequence, I couldn't find the "s" symbol.

 

See the link in the SteveL27 post 6. That link includes a formula for the nth term of the series. I don't think there is a more detailed treatment than that.