Odd prime sum limit: Difference between revisions

Line 4:

== Comparison with odd limit ==

The 1- and 2-odd-prime-sum-limit are equivalent to the [[1-odd-limit]], which only contains a single interval pair {[[1/1]], [[2/1]]}. The 3- and 4-odd-prime-sum-limit are equivalent to the [[3-odd-limit]], which adds {[[3/2]], [[4/3]]}. All edos are consistent in those limits.

The 5-odd-prime-sum-limit adds {[[5/4]], [[8/5]]} without {[[5/3]], [[6/5]]} from the [[5-odd-limit]], so it is the first OPSL that differs from the corresponding odd limit. The 6-odd-prime-sum-limit adds {[[9/8]], [[16/9]]}. The 7-odd-prime-sum-limit adds {[[7/4]], [[8/7]]} without {[[7/6]], [[12/7]]}, and the 8-odd-prime-sum-limit adds {5/3, 6/5} as well as {[[15/8]], [[16/15]]}. The 9-odd-prime-sum-limit adds {[[27/16]], [[32/27]]}, and the 10-odd-prime-sum-limit adds {7/6, 12/7}, {[[21/16]], [[32/21]]}, and {[[25/16]], [[32/25]]}. The 11-odd-prime-sum-limit adds {[[11/8]], [[16/11]]}, {[[9/5]], [[10/9]]}, and {[[45/32]], [[64/45]]}. The 12-odd-prime-sum-limit adds {[[7/5]], [[10/7]]}, {[[35/32]], [[64/35]]} and {[[81/64]], [[128/81]]}.

== Minimal OPSL-consistent edos ==

Line 123:

|}

<nowiki>*</nowiki>apart from 0edo

== Whole-interval OPSL ==

The ''n''-whole-interval-OPSL, or '''''n''-WOPSL''', is slightly different from the ''n''-OPSL. This is the collection of all just ratios with a no-twos [[Wilson height]] that does not exceed the integer ''n''. It was confused with the original definition for ''n''-OPSL at the time of this Wiki article's creation, but has since been corrected.

=== Comparison between odd-limit and WOPSL ===

The 1- and 2-WOPSL are equivalent to the [[1-odd-limit]], which only contains a single interval pair {[[1/1]], [[2/1]]}. The 3- and 4-WOPSL are equivalent to the [[3-odd-limit]], which adds {[[3/2]], [[4/3]]}. All edos are consistent in those limits.

The 5-WOPSL adds {[[5/4]], [[8/5]]} without {[[5/3]], [[6/5]]} from the [[5-odd-limit]], so it is the first WOPSL that differs from the corresponding odd limit. The 6-WOPSL adds {[[9/8]], [[16/9]]}. The 7-WOPSL adds {[[7/4]], [[8/7]]} without {[[7/6]], [[12/7]]}, and the 8-WOPSL adds {5/3, 6/5} as well as {[[15/8]], [[16/15]]}. The 9-WOPSL adds {[[27/16]], [[32/27]]}, and the 10-WOPSL adds {7/6, 12/7}, {[[21/16]], [[32/21]]}, and {[[25/16]], [[32/25]]}. The 11-WOPSL adds {[[11/8]], [[16/11]]}, {[[9/5]], [[10/9]]}, and {[[45/32]], [[64/45]]}. The 12-WOPSL adds {[[7/5]], [[10/7]]}, {[[35/32]], [[64/35]]} and {[[81/64]], [[128/81]]}.

[[Category:Limit]]

[[Category:Terms]]

@@ Line 4: / Line 4: @@
 == Comparison with odd limit ==
 The 1- and 2-odd-prime-sum-limit are equivalent to the [[1-odd-limit]], which only contains a single interval pair {[[1/1]], [[2/1]]}. The 3- and 4-odd-prime-sum-limit are equivalent to the [[3-odd-limit]], which adds {[[3/2]], [[4/3]]}. All edos are consistent in those limits.
 The 5-odd-prime-sum-limit adds {[[5/4]], [[8/5]]} without {[[5/3]], [[6/5]]} from the [[5-odd-limit]], so it is the first OPSL that differs from the corresponding odd limit. The 6-odd-prime-sum-limit adds {[[9/8]], [[16/9]]}. The 7-odd-prime-sum-limit adds {[[7/4]], [[8/7]]} without {[[7/6]], [[12/7]]}, and the 8-odd-prime-sum-limit adds {5/3, 6/5} as well as {[[15/8]], [[16/15]]}. The 9-odd-prime-sum-limit adds {[[27/16]], [[32/27]]}, and the 10-odd-prime-sum-limit adds {7/6, 12/7}, {[[21/16]], [[32/21]]}, and {[[25/16]], [[32/25]]}. The 11-odd-prime-sum-limit adds {[[11/8]], [[16/11]]}, {[[9/5]], [[10/9]]}, and {[[45/32]], [[64/45]]}. The 12-odd-prime-sum-limit adds {[[7/5]], [[10/7]]}, {[[35/32]], [[64/35]]} and {[[81/64]], [[128/81]]}.
 == Minimal OPSL-consistent edos ==
@@ Line 123: / Line 123: @@
 |}
 <nowiki>*</nowiki>apart from 0edo
+== Whole-interval OPSL ==
+The ''n''-whole-interval-OPSL, or '''''n''-WOPSL''', is slightly different from the ''n''-OPSL. This is the collection of all just ratios with a no-twos [[Wilson height]] that does not exceed the integer ''n''. It was confused with the original definition for ''n''-OPSL at the time of this Wiki article's creation, but has since been corrected.
+=== Comparison between odd-limit and WOPSL ===
+The 1- and 2-WOPSL are equivalent to the [[1-odd-limit]], which only contains a single interval pair {[[1/1]], [[2/1]]}. The 3- and 4-WOPSL are equivalent to the [[3-odd-limit]], which adds {[[3/2]], [[4/3]]}. All edos are consistent in those limits.
+The 5-WOPSL adds {[[5/4]], [[8/5]]} without {[[5/3]], [[6/5]]} from the [[5-odd-limit]], so it is the first WOPSL that differs from the corresponding odd limit. The 6-WOPSL adds {[[9/8]], [[16/9]]}. The 7-WOPSL adds {[[7/4]], [[8/7]]} without {[[7/6]], [[12/7]]}, and the 8-WOPSL adds {5/3, 6/5} as well as {[[15/8]], [[16/15]]}. The 9-WOPSL adds {[[27/16]], [[32/27]]}, and the 10-WOPSL adds {7/6, 12/7}, {[[21/16]], [[32/21]]}, and {[[25/16]], [[32/25]]}. The 11-WOPSL adds {[[11/8]], [[16/11]]}, {[[9/5]], [[10/9]]}, and {[[45/32]], [[64/45]]}. The 12-WOPSL adds {[[7/5]], [[10/7]]}, {[[35/32]], [[64/35]]} and {[[81/64]], [[128/81]]}.
 [[Category:Limit]]
 [[Category:Terms]]