List of superparticular intervals: Difference between revisions

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The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<sup>2</sup>*3<sup>2</sup>)/(5*7), while 37/36 would belong to the 37-limit.

[~~http~~:~~//en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem~~ Størmer's theorem] ~~guarantees~~ that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than [[2/1]], [[3/2]], [[4/3]], and [[9/8]]. ~~[http://oeis.org/~~A002071 ~~A002071 -- OEIS]~~ gives the number of superparticular ratios in each prime limit, ~~[http://oeis.org/~~A145604 ~~A145604 - OEIS]~~ shows the increment from limit to limit, and ~~[http://oeis.org/~~A117581 ~~A117581]~~ the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).

[[Wikipedia:Størmer's theorem|Størmer's theorem]] states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than [[2/1]], [[3/2]], [[4/3]], and [[9/8]]. {{OEIS|A002071}} gives the number of superparticular ratios in each prime limit, {{OEIS|A145604}} shows the increment from limit to limit, and {{OEIS|A117581}} gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).

See also [[gallery of just intervals]]. Many of the names below come from [http://www.huygens-fokker.org/docs/intervals.html here].

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 The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<sup>2</sup>*3<sup>2</sup>)/(5*7), while 37/36 would belong to the 37-limit.
-[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem Størmer's theorem] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than [[2/1]], [[3/2]], [[4/3]], and [[9/8]]. [http://oeis.org/A002071 A002071 &#45;- OEIS] gives the number of superparticular ratios in each prime limit, [http://oeis.org/A145604 A145604 &#45; OEIS] shows the increment from limit to limit, and [http://oeis.org/A117581 A117581] the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).
+[[Wikipedia:Størmer's theorem|Størmer's theorem]] states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than [[2/1]], [[3/2]], [[4/3]], and [[9/8]]. {{OEIS|A002071}} gives the number of superparticular ratios in each prime limit, {{OEIS|A145604}} shows the increment from limit to limit, and {{OEIS|A117581}} gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).
 See also [[gallery of just intervals]]. Many of the names below come from [http://www.huygens-fokker.org/docs/intervals.html here].