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Math Help - Finding a formula for this data

  1. #1
    Newbie
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    Oct 2009
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    Finding a formula for this data

    I'm trying to work out a formula (i dont even know if it possibly exists) but this is the information is have:
    The 1st term - 1
    The 2nd term - 1
    3rd - 1
    4th - 2
    5th - 2
    6th - 2
    7th - 2
    8th - 2
    9th - 3
    10th - 3
    etc, etc, but basically i realise that the pattern is you square root the term and round down, eg, if u wanted to find the 29th term, u squeare root, so u get 5.39 and round down to 5, so the 29th term is 5.
    What i need to know is there a formula for this, not matter how complicated???
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  2. #2
    Super Member
    Joined
    Jan 2009
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    Quote Originally Posted by andy450 View Post
    I'm trying to work out a formula (i dont even know if it possibly exists) but this is the information is have:
    The 1st term - 1
    The 2nd term - 1
    3rd - 1
    4th - 2
    5th - 2
    6th - 2
    7th - 2
    8th - 2
    9th - 3
    10th - 3
    etc, etc, but basically i realise that the pattern is you square root the term and round down, eg, if u wanted to find the 29th term, u squeare root, so u get 5.39 and round down to 5, so the 29th term is 5.
    What i need to know is there a formula for this, not matter how complicated???
    is there a formula for this
    Yes.
    A floor function or greatest integer function is needed (for rounding down).

     f(x) = INT \left( \sqrt{x} \, \right )

    .
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  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
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    Quote Originally Posted by aidan View Post
    Yes.
    A floor function or greatest integer function is needed (for rounding down).

     f(x) = INT \left( \sqrt{x} \, \right )

    .
    The floor function even has its own notation:

    \lfloor \sqrt{x} \rfloor denotes the greatest integer less than \sqrt{x}

    There is also the similar ceiling function - the least integer greater than ..

    so for \sqrt{x} this would be writtem \lceil \sqrt{x} \,\rceil.



    CB
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