Naturally, having revisited the odd (+) and even (-) algorithm and using Gemini to generate new code, the next step was to revisit the odd (-) and even (+) algorithm. In this latter algorithm, the sum of the even digits is added to the number while the sum of the odd digits is subtracted. In both cases, the attractors remain the sum but the vortices and captives will differ. Here a permalink to the SageMathCell code that will catalog the numbers from 0 to 40000. Here is a link to the code that Gemini created. I've put the output in a Google document for later reference.
Gemini asked if I'd like to generate a comparison table for the two algorithms. Here a permalink to the algorithm that it created and a link to the code in Gemini itself. Figure 1 shows the output for the range up to 40000. I also asked about the discrepancy in the count of attractors as they should be the same. Here is a link to Gemini's explanation.
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Figure 1 |
As can be seen, even though the attractors are the same in both cases, the number of captives that they gather can be vastly different. The attractor 8987 claims 617 captives (the record) with odd (-) and even (+) but none at all with odd (+) and even (-).
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