# Discovering formula for a sequence with recurring digits

spiritzavior
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.

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),...

ramsey2879
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.

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.

ppnl
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...

ramsey2879
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.

spiritzavior
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,...

spiritzavior
$\left\{\left\{k\right\}^{2n}_{k=1}\right\}^{∞}_{n=1}$