User:BudjarnLambeth/Basal subgroup: Difference between revisions
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m BudjarnLambeth moved page Basal subgroup to User:BudjarnLambeth/Basal subgroup |
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=== ed3/2, ed5/2, ed7/2, ed11/2... === | === ed3/2, ed5/2, ed7/2, ed11/2... === | ||
A.k.a. "[[half-prime subgroup]]s". | A.k.a. "[[half-prime subgroup]]s". | ||
To find BSGn/2: | To find BSGn/2: | ||
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# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/2 | |||
# Add n/2 to the start of the subgroup | # Add n/2 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
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# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/3 | |||
# Add n/3 to the start of the subgroup | # Add n/3 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
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# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/4 | |||
# Add n/4 to the start of the subgroup | # Add n/4 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 375: | Line 377: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/5 | |||
# Add n/5 to the start of the subgroup | # Add n/5 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
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'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed6/5]]''' - - - BSG6/5 - - - is 6 | * The basal subgroup of '''[[ed6/5]]''' - - - BSG6/5 - - - is 6/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed8/5]]''' - - - BSG8/5 - - - is 8 | * The basal subgroup of '''[[ed8/5]]''' - - - BSG8/5 - - - is 8/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed9/5]]''' - - - BSG9/5 - - - is 9 | * The basal subgroup of '''[[ed9/5]]''' - - - BSG9/5 - - - is 9/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed12/5]]''' - - - BSG12/5 - - - is 12 | * The basal subgroup of '''[[ed12/5]]''' - - - BSG12/5 - - - is 12/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed14/5]]''' - - - BSG14/5 - - - is 14/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | * The basal subgroup of '''[[ed14/5]]''' - - - BSG14/5 - - - is 14/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
* The basal subgroup of '''[[ed16/5]]''' - - - BSG16/5 - - - is 16/5 . 3/5 . | * The basal subgroup of '''[[ed16/5]]''' - - - BSG16/5 - - - is 16/5 . 3/5 . 7/5 . 11/5 . 13/5 . 17/5... | ||
* The basal subgroup of '''[[ed18/5]]''' - - - BSG18/5 - - - is 18 | * The basal subgroup of '''[[ed18/5]]''' - - - BSG18/5 - - - is 18/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed21/5]]''' - - - BSG21/5 - - - is 21/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | * The basal subgroup of '''[[ed21/5]]''' - - - BSG21/5 - - - is 21/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
* The basal subgroup of '''[[ed22/5]]''' - - - BSG22/5 - - - is 22/5 . 13/5 . 17/5 . 19/5 . 23/5 . 29/5... | * The basal subgroup of '''[[ed22/5]]''' - - - BSG22/5 - - - is 22/5 . 13/5 . 17/5 . 19/5 . 23/5 . 29/5... | ||
* The basal subgroup of '''[[ed24/5]]''' - - - BSG24/5 - - - is 24 | * The basal subgroup of '''[[ed24/5]]''' - - - BSG24/5 - - - is 24/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed26/5]]''' - - - BSG26/5 - - - is 26/5 . 17/5 . 19/5 . 23/5 . 29/5 . 31/5... | * The basal subgroup of '''[[ed26/5]]''' - - - BSG26/5 - - - is 26/5 . 17/5 . 19/5 . 23/5 . 29/5 . 31/5... | ||
* The basal subgroup of '''[[ed27/5]]''' - - - BSG27/5 - - - is 27 | * The basal subgroup of '''[[ed27/5]]''' - - - BSG27/5 - - - is 27/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed28/5]]''' - - - BSG28/5 - - - is 28/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | * The basal subgroup of '''[[ed28/5]]''' - - - BSG28/5 - - - is 28/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
''and so on...'' | ''and so on...'' | ||
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# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/6 | |||
# Add n/6 to the start of the subgroup | # Add n/6 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 422: | Line 426: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/7 | |||
# Add n/7 to the start of the subgroup | # Add n/7 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 451: | Line 456: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/8 | |||
# Add n/8 to the start of the subgroup | # Add n/8 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
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# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/9 | |||
# Add n/9 to the start of the subgroup | # Add n/9 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 494: | Line 501: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/10 | |||
# Add n/10 to the start of the subgroup | # Add n/10 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
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=== ed12/11, ed14/11, ed15/11, ed16/11... === | === ed12/11, ed14/11, ed15/11, ed16/11... === | ||
A.k.a. "[[half-prime subgroup| | A.k.a. "[[half-prime subgroup|eleventh-prime subgroups]]". | ||
To find BSGn/11: | To find BSGn/11: | ||
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# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/11 | |||
# Add n/11 to the start of the subgroup | # Add n/11 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 541: | Line 550: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/12 | |||
# Add n/12 to the start of the subgroup | # Add n/12 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 558: | Line 568: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/13 | |||
# Add n/13 to the start of the subgroup | # Add n/13 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 583: | Line 594: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/14 | |||
# Add n/14 to the start of the subgroup | # Add n/14 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 600: | Line 612: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/15 | |||
# Add n/15 to the start of the subgroup | # Add n/15 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||