What is the correct term for a nonrepeating cyclic sequence?

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I was looking for a way to produce pseudo-random numbers within a certain range that do not repeat and I came up with the following formula:



$x_n = (x_n-1 + s) mod r$



This has the property that, when $s$ and $r$ are coprime, $x$ does not repeat with $r$ iterations.



For example, consider:



$r = 10, s = 7, x_0 = 0$



$x_1 = (0 + 7) mod 10 = 7$



$x_2 = (7 + 7) mod 10 = 4$



$x_3 = (4 + 7) mod 10 = 1$



And so on. The full sequence is: $0, 7, 4, 1, 8, 5, 2, 9, 6, 3$. As you can see, it is pseudo-random-ish. With larger, well-chosen values of $r$ and $s$ the relationship between the numbers is less obvious.



I have two questions about this:



First, does this formula have a name (and if so, what is it)?



Second, what is the proper term for this type of sequence? I've tried searching with variations on "nonrepeating cyclic sequence" but not found what I'm looking for. The main characteristic that I'm looking for is that the numbers in the sequence must not repeat until all of the numbers in the range have been output. Ultimately, I'd like to find sequences where the relationship between the numbers is not obvious (pseudo-random).




sequences-and-series




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    I was looking for a way to produce pseudo-random numbers within a certain range that do not repeat and I came up with the following formula:



    $x_n = (x_n-1 + s) mod r$



    This has the property that, when $s$ and $r$ are coprime, $x$ does not repeat with $r$ iterations.



    For example, consider:



    $r = 10, s = 7, x_0 = 0$



    $x_1 = (0 + 7) mod 10 = 7$



    $x_2 = (7 + 7) mod 10 = 4$



    $x_3 = (4 + 7) mod 10 = 1$



    And so on. The full sequence is: $0, 7, 4, 1, 8, 5, 2, 9, 6, 3$. As you can see, it is pseudo-random-ish. With larger, well-chosen values of $r$ and $s$ the relationship between the numbers is less obvious.



    I have two questions about this:



    First, does this formula have a name (and if so, what is it)?



    Second, what is the proper term for this type of sequence? I've tried searching with variations on "nonrepeating cyclic sequence" but not found what I'm looking for. The main characteristic that I'm looking for is that the numbers in the sequence must not repeat until all of the numbers in the range have been output. Ultimately, I'd like to find sequences where the relationship between the numbers is not obvious (pseudo-random).




    sequences-and-series




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I was looking for a way to produce pseudo-random numbers within a certain range that do not repeat and I came up with the following formula:



      $x_n = (x_n-1 + s) mod r$



      This has the property that, when $s$ and $r$ are coprime, $x$ does not repeat with $r$ iterations.



      For example, consider:



      $r = 10, s = 7, x_0 = 0$



      $x_1 = (0 + 7) mod 10 = 7$



      $x_2 = (7 + 7) mod 10 = 4$



      $x_3 = (4 + 7) mod 10 = 1$



      And so on. The full sequence is: $0, 7, 4, 1, 8, 5, 2, 9, 6, 3$. As you can see, it is pseudo-random-ish. With larger, well-chosen values of $r$ and $s$ the relationship between the numbers is less obvious.



      I have two questions about this:



      First, does this formula have a name (and if so, what is it)?



      Second, what is the proper term for this type of sequence? I've tried searching with variations on "nonrepeating cyclic sequence" but not found what I'm looking for. The main characteristic that I'm looking for is that the numbers in the sequence must not repeat until all of the numbers in the range have been output. Ultimately, I'd like to find sequences where the relationship between the numbers is not obvious (pseudo-random).




      sequences-and-series




      share|cite|improve this question











      I was looking for a way to produce pseudo-random numbers within a certain range that do not repeat and I came up with the following formula:



      $x_n = (x_n-1 + s) mod r$



      This has the property that, when $s$ and $r$ are coprime, $x$ does not repeat with $r$ iterations.



      For example, consider:



      $r = 10, s = 7, x_0 = 0$



      $x_1 = (0 + 7) mod 10 = 7$



      $x_2 = (7 + 7) mod 10 = 4$



      $x_3 = (4 + 7) mod 10 = 1$



      And so on. The full sequence is: $0, 7, 4, 1, 8, 5, 2, 9, 6, 3$. As you can see, it is pseudo-random-ish. With larger, well-chosen values of $r$ and $s$ the relationship between the numbers is less obvious.



      I have two questions about this:



      First, does this formula have a name (and if so, what is it)?



      Second, what is the proper term for this type of sequence? I've tried searching with variations on "nonrepeating cyclic sequence" but not found what I'm looking for. The main characteristic that I'm looking for is that the numbers in the sequence must not repeat until all of the numbers in the range have been output. Ultimately, I'd like to find sequences where the relationship between the numbers is not obvious (pseudo-random).





      sequences-and-series





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 23 at 21:04









      Jack A.

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