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Old 2022-03-16, 21:33   #1
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"Ed Hall"
Dec 2009
Adirondack Mtns

19×257 Posts
Default Some Somewhat Easier n^i Sequences Available for Termination

In the sub-project Aliquot sequences that start on the integer powers n^i, there are some sequences that should terminate with a prime. This thread will list those with a current term that is less than 145 digits* and flagged as unreserved. These sequences are mostly above those of the main project, although some may drop into the main project on their way to termination.**

If you are interested in the excitement of terminating an Aliquot Sequence, although not guaranteed, these are pretty sure bets to do so.

Note: For anyone, new or old that would like to automate some of their work, please look at the script in post 7 below. The script can be used with Aliqueit to convert the base^exponent value to its decimal and invoke Aliqueit to run the sequence and upload the results.

Please visit the thread mentioned above and its associated page for more details. You may reserve the available sequences in this thread and see the current status on the project pages, as updates are applied.

As an example of an available sequence, 66^92 is the smallest as of the latest full edit, and has a 136 digit term with a composite cofactor of 136 digits.

It is suggested that if you will take more than a day (or two) to terminate a sequence, you reserve it, so others don't duplicate your work. The following are the current reservations (but, also check the latest posts):

As of the time of the last edit (fiddling), the following sequences were available:

The second value is the cofactor size.

Here's a size sorted listing of the above:

* The current threshold of 145 digits was chosen to ensure the listing has at least a fair number of sequences, with some more challenging.

** Sequences of the type n^i where both n and i are either odd or even (matched parity) nearly always terminate. Also, sequences where n is double a perfect square nearly always terminate. On occasion one will merge with a sequence in the main project and become open-ended.

The following are the terminated sequences that have not yet been updated in the tables. Many have unknown credit for termination (listed as A). If "The Terminator" would like credit, please claim it in this or the other thread:
21^121: Prime - GDB
63^91: Prime - GDB
66^92: Prime - GDB
191^83: Prime - GDB
269^69: Prime - GDB
284^64: Prime - GDB
331^65: Prime - GDB
337^57: Prime - GDB
337^59: Prime - GDB
347^57: Prime - GDB
347^61: Prime - GDB
347^65: Prime - GDB
349^57: Prime - GDB
385^65: Prime - GDB
780^52: Prime - GDB

Last fiddled with by EdH on 2022-09-28 at 12:52 Reason: Updates
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