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Thread: Finding a formula for a sequence

  1. #1
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    Finding a formula for a sequence

    Can anyone please help me find a formula for this sequence:

    4, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12...

    It's based on fewest number of 2-blocks required to surround an increasing number of 1-blocks.
    I've tried the method where you find differences between terms (up to 6 columns worth), but cannot get it to resolve to one value. Does this mean that it isn't quadratic?

    Tried using Excel to find a line of best fit and a 'moving average' line fits really well. Still didn't help me derive a formula.

    Any help would be greatly appreciated!
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  2. #2
    MHF Contributor
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    Re: Finding a formula for a sequence

    $3+\lceil 2\sqrt{n}-1\rceil $

    That is the smallest integer no smaller than the number, also known as the ceiling function. Example:
    $\lceil 1.1\rceil = \lceil 1.9 \rceil = \lceil 2 \rceil = 2$

    In general, this website is very useful.

    https://oeis.org/search?q=1%2C2%2C3%...lish&go=Search

    I used your sequence shifted down 3, so that's why it is 3+...
    Last edited by SlipEternal; Dec 20th 2017 at 06:05 PM.
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