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S-expression: Difference between revisions

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→Sk/S(k + 1) (ultraparticulars): complete the subgroup column
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! Interval relation
! Interval relation
! Ratio
! Ratio
! Prime limit
! Subgroup
|-
|-
| S2⋅S3
| S2⋅S3
| ([[3/1]])/([[2/1]])
| ([[3/1]])/([[2/1]])
| [[3/2]]
| [[3/2]]
| 3
| 2.3
|-
|-
| S3⋅S4
| S3⋅S4
| ([[3/2]])/([[5/4]])
| ([[3/2]])/([[5/4]])
| [[6/5]]
| [[6/5]]
| 5
| 2.3.5
|-
|-
| S4⋅S5
| S4⋅S5
| ([[4/3]])/([[6/5]])
| ([[4/3]])/([[6/5]])
| [[10/9]]
| [[10/9]]
| 5
| 2.3.5
|-
|-
| S5⋅S6
| S5⋅S6
| ([[5/4]])/([[7/6]])
| ([[5/4]])/([[7/6]])
| [[15/14]]
| [[15/14]]
| 7
| 2.3.5.7
|-
|-
| S6⋅S7
| S6⋅S7
| ([[6/5]])/([[8/7]])
| ([[6/5]])/([[8/7]])
| [[21/20]]
| [[21/20]]
| 7
| 2.3.5.7
|-
|-
| S7⋅S8
| S7⋅S8
| ([[7/6]])([[9/8]])
| ([[7/6]])([[9/8]])
| [[28/27]]
| [[28/27]]
| 7
| 2.3.7
|-
|-
| S8⋅S9
| S8⋅S9
| ([[8/7]])/([[10/9]])
| ([[8/7]])/([[10/9]])
| [[36/35]]
| [[36/35]]
| 7
| 2.3.5.7
|-
|-
| S9⋅S10
| S9⋅S10
| ([[9/8]])/([[11/10]])
| ([[9/8]])/([[11/10]])
| [[45/44]]
| [[45/44]]
| 11
| 2.3.5.11
|-
|-
| S10⋅S11
| S10⋅S11
| ([[10/9]])/([[12/11]])
| ([[10/9]])/([[12/11]])
| [[55/54]]
| [[55/54]]
| 11
| 2.3.5.11
|-
|-
| S11⋅S12
| S11⋅S12
| ([[11/10]])/([[13/12]])
| ([[11/10]])/([[13/12]])
| [[66/65]]
| [[66/65]]
| 13
| 2.3.5.11.13
|-
|-
| S12⋅S13
| S12⋅S13
| ([[12/11]])/([[14/13]])
| ([[12/11]])/([[14/13]])
| [[78/77]]
| [[78/77]]
| 13
| 2.3.7.11.13
|-
|-
| S13⋅S14
| S13⋅S14
| ([[13/12]])/([[15/14]])
| ([[13/12]])/([[15/14]])
| [[91/90]]
| [[91/90]]
| 13
| 2.3.5.7.13
|-
|-
| S14⋅S15
| S14⋅S15
| ([[14/13]])/([[16/15]])
| ([[14/13]])/([[16/15]])
| [[105/104]]
| [[105/104]]
| 13
| 2.3.5.7.13
|-
|-
| S15⋅S16
| S15⋅S16
| ([[15/14]])/([[17/16]])
| ([[15/14]])/([[17/16]])
| [[120/119]]
| [[120/119]]
| 17
| 2.3.5.7.17
|-
|-
| S16⋅S17
| S16⋅S17
| ([[16/15]])/([[18/17]])
| ([[16/15]])/([[18/17]])
| [[136/135]]
| [[136/135]]
| 17
| 2.3.5.17
|-
|-
| S17⋅S18
| S17⋅S18
| ([[17/16]])/([[19/18]])
| ([[17/16]])/([[19/18]])
| [[153/152]]
| [[153/152]]
| 19
| 2.3.17.19
|-
|-
| S18⋅S19
| S18⋅S19
| ([[18/17]])/([[20/19]])
| ([[18/17]])/([[20/19]])
| [[171/170]]
| [[171/170]]
| 19
| 2.3.5.17.19
|-
|-
| S19⋅S20
| S19⋅S20
| ([[19/18]])/([[21/20]])
| ([[19/18]])/([[21/20]])
| [[190/189]]
| [[190/189]]
| 19
| 2.3.5.7.19
|-
|-
| S20⋅S21
| S20⋅S21
| ([[20/19]])/([[22/21]])
| ([[20/19]])/([[22/21]])
| [[210/209]]
| [[210/209]]
| 19
| 2.3.5.7.11.19
|-
|-
| S21⋅S22
| S21⋅S22
| ([[21/20]])/([[23/22]])
| ([[21/20]])/([[23/22]])
| [[231/230]]
| [[231/230]]
| 23
| 2.3.5.7.11.23
|-
|-
| S22⋅S23
| S22⋅S23
| ([[22/21]])/([[24/23]])
| ([[22/21]])/([[24/23]])
| [[253/252]]
| [[253/252]]
| 23
| 2.3.5.7.11.23
|-
|-
| S23⋅S24
| S23⋅S24
| ([[23/22]])/([[25/24]])
| ([[23/22]])/([[25/24]])
| [[276/275]]
| [[276/275]]
| 23
| 2.3.5.11.23
|-
|-
| S24⋅S25
| S24⋅S25
| ([[24/23]])/([[26/25]])
| ([[24/23]])/([[26/25]])
| [[300/299]]
| [[300/299]]
| 23
| 2.3.5.13.23
|-
|-
| S25⋅S26
| S25⋅S26
| ([[25/24]])/([[27/26]])
| ([[25/24]])/([[27/26]])
| [[325/324]]
| [[325/324]]
| 13
| 2.3.5.13
|-
|-
| S26⋅S27
| S26⋅S27
| ([[26/25]])/([[28/27]])
| ([[26/25]])/([[28/27]])
| [[351/350]]
| [[351/350]]
| 13
| 2.3.5.7.13
|-
|-
| S27⋅S28
| S27⋅S28
| ([[27/26]])/([[29/28]])
| ([[27/26]])/([[29/28]])
| [[378/377]]
| [[378/377]]
| 29
| 2.3.5.7.13.29
|-
|-
| S28⋅S29
| S28⋅S29
| ([[28/27]])/([[30/29]])
| ([[28/27]])/([[30/29]])
| [[406/405]]
| [[406/405]]
| 29
| 2.3.5.7.29
|-
|-
| S29⋅S30
| S29⋅S30
| ([[29/28]])/([[31/30]])
| ([[29/28]])/([[31/30]])
| [[435/434]]
| [[435/434]]
| 31
| 2.3.5.7.29.31
|-
|-
| S30⋅S31
| S30⋅S31
| ([[30/29]])/([[32/31]])
| ([[30/29]])/([[32/31]])
| [[465/464]]
| [[465/464]]
| 31
| 2.3.5.29.31
|-
|-
| S31⋅S32
| S31⋅S32
| ([[31/30]])/([[33/32]])
| ([[31/30]])/([[33/32]])
| [[496/495]]
| [[496/495]]
| 31
| 2.3.5.11.31
|-
|-
| S32⋅S33
| S32⋅S33
| ([[32/31]])/([[34/33]])
| ([[32/31]])/([[34/33]])
| [[528/527]]
| [[528/527]]
| 31
| 2.3.11.17.31
|-
|-
| S33⋅S34
| S33⋅S34
| ([[33/32]])/([[35/34]])
| ([[33/32]])/([[35/34]])
| [[561/560]]
| [[561/560]]
| 17
| 2.3.5.7.11.17
|-
|-
| S34⋅S35
| S34⋅S35
| ([[34/33]])/([[36/35]])
| ([[34/33]])/([[36/35]])
| [[595/594]]
| [[595/594]]
| 17
| 2.3.5.7.11.17
|-
|-
| S49⋅S50
| S49⋅S50
| ([[49/48]])/([[51/50]])
| ([[49/48]])/([[51/50]])
| [[1225/1224]]
| [[1225/1224]]
| 17
| 2.3.5.7.17
|-
|-
| S50⋅S51
| S50⋅S51
| ([[50/49]])/([[52/51]])
| ([[50/49]])/([[52/51]])
| [[1275/1274]]
| [[1275/1274]]
| 17
| 2.3.5.7.13.17
|-
|-
| S55⋅S56
| S55⋅S56
| ([[55/54]])/([[57/56]])
| ([[55/54]])/([[57/56]])
| [[1540/1539]]
| [[1540/1539]]
| 19
| 2.3.5.7.11.19
|-
|-
| S63⋅S64
| S63⋅S64
| ([[63/62]])/([[65/64]])
| ([[63/62]])/([[65/64]])
| [[2016/2015]]
| [[2016/2015]]
| 31
| 2.3.5.7.13.31
|-
|-
| S64⋅S65
| S64⋅S65
| ([[64/63]])/([[66/65]])
| ([[64/63]])/([[66/65]])
| [[2080/2079]]
| [[2080/2079]]
| 13
| 2.3.5.7.11.13
|-
|-
| S76⋅S77
| S76⋅S77
| ([[76/75]])/([[78/77]])
| ([[76/75]])/([[78/77]])
| [[2926/2925]]
| [[2926/2925]]
| 19
| 2.3.5.7.11.13.19
|-
|-
| S91⋅S92
| S91⋅S92
| ([[91/90]])/([[93/92]])
| ([[91/90]])/([[93/92]])
| [[4186/4185]]
| [[4186/4185]]
| 31
| 2.3.5.7.13.23.31
|-
|-
| S115⋅S116
| <small>S115⋅S116</small>
| ([[115/114]])/([[117/116]])
| <small>([[115/114]])/([[117/116]])</small>
| [[6670/6669]]
| [[6670/6669]]
| 29
| 2.3.5.13.19.23.29
|-
|-
| S153⋅S154
| <small>S153⋅S154</small>
| ([[153/152]])/([[155/154]])
| <small>([[153/152]])/([[155/154]])</small>
| [[11781/11780]]
| <small>[[11781/11780]]</small>
| 31
| 2.3.5.7.11.17.19.31
|-
|-
| S154⋅S155
| <small>S154⋅S155</small>
| ([[154/153]])/([[156/155]])
| <small>([[154/153]])/([[156/155]])</small>
| [[11935/11934]]
| <small>[[11935/11934]]</small>
| 31
| 2.3.5.7.11.13.17.31
|-
|-
| S169⋅S170
| <small>S169⋅S170</small>
| ([[169/168]])/([[171/170]])
| <small>([[169/168]])/([[171/170]])</small>
| [[14365/14364]]
| <small>[[14365/14364]]</small>
| 19
| 2.3.5.7.13.17.19
|-
|-
| S208⋅S209
| <small>S208⋅S209</small>
| ([[208/207]])/([[210/209]])
| <small>([[208/207]])/([[210/209]])</small>
| [[21736/21735]]
| <small>[[21736/21735]]</small>
| 19
| 2.3.5.7.11.13.19
|-
|-
| S323⋅S324
| <small>S323⋅S324</small>
| ([[323/322]])/([[325/324]])
| <small>([[323/322]])/([[325/324]])</small>
| [[52326/52325]]
| <small>[[52326/52325]]</small>
| 23
| 2.3.5.7.13.17.19.23
|-
|-
| S341⋅S342
| <small>S341⋅S342</small>
| ([[341/340]])/([[343/342]])
| <small>([[341/340]])/([[343/342]])</small>
| [[58311/58310]]
| <small>[[58311/58310]]</small>
| 31
| 2.3.5.7.11.17.19.31
|-
|-
| S494⋅S495
| <small>S494⋅S495</small>
| ([[494/493]])/([[496/495]])
| <small>([[494/493]])/([[496/495]])</small>
| [[122265/122264]]
| <small>[[122265/122264]]</small>
| 31
| 2.3.5.7.11.13.19.29.31
|-
|-
| S1519⋅S1520
| <small>S1519⋅S1520</small>
| ([[1519/1518]])/([[1521/1520]])
| <small>([[1519/1518]])/([[1521/1520]])</small>
| [[1154440/1154439]]
| <small>[[1154440/1154439]]</small>
| 31
| 2.3.5.7.11.13.19.23.31
|}
|}


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