# Discovering formula for a sequence with recurring digits

## Main Question or Discussion Point

please guide me on how to discover the formula for this sequence --> 1,2,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,7,8,...

responses are highly appreciated.

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coolul007
Gold Member
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),...

please guide me on how to discover the formula for this sequence --> 1,2,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,7,8,...

responses are highly appreciated.
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.

coolul007
Gold Member
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.

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.
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.......

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.......
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.

my bad, it should be a sequence of numbers not just digits.

what i really mean as a sequence is this 1,2,1,2,3,4,1,2,3,4,5,6,...,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,...

coolul007
Gold Member
$\left\{\left\{k\right\}^{2n}_{k=1}\right\}^{∞}_{n=1}$

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.