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: | ||
| Line 52: | Line 51: | ||
=== ed5/3, ed7/3, ed11/3, ed17/3... === | === ed5/3, ed7/3, ed11/3, ed17/3... === | ||
A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | ||
To find BSGn/3: | To find BSGn/3: | ||
| Line 72: | Line 70: | ||
=== ed5/4, ed7/4, ed11/4, ed17/4... === | === ed5/4, ed7/4, ed11/4, ed17/4... === | ||
A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | ||
To find BSGn/4: | To find BSGn/4: | ||
| Line 92: | Line 89: | ||
=== ed7/5, ed11/5, ed17/5, ed19/5... === | === ed7/5, ed11/5, ed17/5, ed19/5... === | ||
A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | ||
To find BSGn/5: | To find BSGn/5: | ||
| Line 111: | Line 107: | ||
=== ed7/6, ed11/6, ed17/6, ed19/6... === | === ed7/6, ed11/6, ed17/6, ed19/6... === | ||
A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | ||
To find BSGn/6: | To find BSGn/6: | ||
| Line 130: | Line 125: | ||
=== ed11/7, ed17/7, ed19/7, ed23/7... === | === ed11/7, ed17/7, ed19/7, ed23/7... === | ||
A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | ||
To find BSGn/7: | To find BSGn/7: | ||
| Line 148: | Line 142: | ||
=== ed11/8, ed17/8, ed19/8, ed23/8... === | === ed11/8, ed17/8, ed19/8, ed23/8... === | ||
A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | ||
To find BSGn/8: | To find BSGn/8: | ||
| Line 166: | Line 159: | ||
=== ed11/9, ed17/9, ed19/9, ed23/9... === | === ed11/9, ed17/9, ed19/9, ed23/9... === | ||
A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | ||
To find BSGn/9: | To find BSGn/9: | ||
| Line 184: | Line 176: | ||
=== ed11/10, ed17/10, ed19/10, ed23/10... === | === ed11/10, ed17/10, ed19/10, ed23/10... === | ||
A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | ||
To find BSGn/10: | To find BSGn/10: | ||
| Line 202: | Line 193: | ||
=== ed13/11, ed17/11, ed19/11, ed23/11... === | === ed13/11, ed17/11, ed19/11, ed23/11... === | ||
A.k.a. "[[half-prime subgroup|eleventh-prime subgroups]]". | A.k.a. "[[half-prime subgroup|eleventh-prime subgroups]]". | ||
To find BSGn/11: | To find BSGn/11: | ||
| Line 219: | Line 209: | ||
=== ed13/12, ed17/12, ed29/12, ed23/12... === | === ed13/12, ed17/12, ed29/12, ed23/12... === | ||
A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | ||
To find BSGn/12: | To find BSGn/12: | ||
| Line 236: | Line 225: | ||
=== ed17/13, ed19/13, ed23/13, ed29/13... === | === ed17/13, ed19/13, ed23/13, ed29/13... === | ||
A.k.a. "[[half-prime subgroup|thirteenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|thirteenth-prime subgroups]]". | ||
To find BSGn/13: | To find BSGn/13: | ||
| Line 252: | Line 240: | ||
=== ed17/14, ed19/14, ed23/14, ed29/14... === | === ed17/14, ed19/14, ed23/14, ed29/14... === | ||
A.k.a. "[[half-prime subgroup|fourteenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fourteenth-prime subgroups]]". | ||
To find BSGn/14: | To find BSGn/14: | ||
| Line 268: | Line 255: | ||
=== ed17/15, ed19/15, ed23/15, ed29/15... === | === ed17/15, ed19/15, ed23/15, ed29/15... === | ||
A.k.a. "[[half-prime subgroup|fifteenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fifteenth-prime subgroups]]". | ||
To find BSGn/15: | To find BSGn/15: | ||
| Line 322: | Line 308: | ||
# 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 | ||
| Line 336: | Line 323: | ||
=== ed4/3, ed8/3, ed10/3, ed14/3... === | === ed4/3, ed8/3, ed10/3, ed14/3... === | ||
A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | ||
To find BSGn/3: | To find BSGn/3: | ||
| Line 343: | Line 329: | ||
# 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 | ||
| Line 363: | Line 350: | ||
=== ed9/4, ed15/4, ed21/4, ed25/4... === | === ed9/4, ed15/4, ed21/4, ed25/4... === | ||
A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | ||
To find BSGn/4: | To find BSGn/4: | ||
| Line 370: | Line 356: | ||
# 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 384: | Line 371: | ||
=== ed6/5, ed8/5, ed9/5, ed12/5... === | === ed6/5, ed8/5, ed9/5, ed12/5... === | ||
A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | ||
To find BSGn/5: | To find BSGn/5: | ||
| Line 391: | 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 | ||
| Line 396: | Line 383: | ||
'''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...'' | ||
| Line 413: | Line 400: | ||
=== ed35/6, ed55/6, ed65/6, ed77/6... === | === ed35/6, ed55/6, ed65/6, ed77/6... === | ||
A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | ||
To find BSGn/6: | To find BSGn/6: | ||
| Line 420: | Line 406: | ||
# 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 433: | Line 420: | ||
=== ed8/7, ed9/7, ed10/7, ed12/7... === | === ed8/7, ed9/7, ed10/7, ed12/7... === | ||
A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | ||
To find BSGn/7: | To find BSGn/7: | ||
| Line 440: | 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 463: | Line 450: | ||
=== ed9/8, ed15/8, ed21/8, ed25/8... === | === ed9/8, ed15/8, ed21/8, ed25/8... === | ||
A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | ||
To find BSGn/8: | To find BSGn/8: | ||
| Line 470: | 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 | ||
| Line 484: | Line 471: | ||
=== ed10/9, ed14/9, ed16/9, ed20/9... === | === ed10/9, ed14/9, ed16/9, ed20/9... === | ||
A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | ||
To find BSGn/9: | To find BSGn/9: | ||
| Line 491: | Line 477: | ||
# 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 508: | Line 495: | ||
=== ed21/10, ed27/10, ed33/10, ed39/10... === | === ed21/10, ed27/10, ed33/10, ed39/10... === | ||
A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | ||
To find BSGn/10: | To find BSGn/10: | ||
| Line 515: | 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 | ||
| Line 527: | Line 514: | ||
=== 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: | ||
| Line 535: | Line 521: | ||
# 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 557: | Line 544: | ||
=== ed35/12, ed55/12, ed65/12, ed77/12... === | === ed35/12, ed55/12, ed65/12, ed77/12... === | ||
A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | ||
To find BSGn/12: | To find BSGn/12: | ||
| Line 564: | 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 581: | 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 606: | 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 623: | 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 | ||