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Discovering formula for a sequence with recurring digits

  1. Aug 31, 2012 #1
    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.
     
  2. jcsd
  3. Aug 31, 2012 #2
    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),...
     
  4. Aug 31, 2012 #3
    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.
     
  5. Aug 31, 2012 #4
    There is either not enough information or the process repeats modulo 10.
     
  6. Aug 31, 2012 #5
    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.......
     
  7. Aug 31, 2012 #6
  8. Aug 31, 2012 #7
    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.
     
  9. Sep 1, 2012 #8
    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,...
     
  10. Sep 6, 2012 #9
    some more detailed answer/s please.
     
  11. Sep 6, 2012 #10
    [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.
     
  12. Sep 6, 2012 #11
    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.
     
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