Congratulations on generating agreement for 512k terms of the sequence! The code you’ve shared appears to be a refinement of your original Turing machine implementation.
Your code generates a binary sequence using the initial “gen” arrays, then expands this sequence exponentially by applying a recursive rule to generate the next “gen” array from the previous one.
The specifics of the rule involve copying the second half of the previous array to both halves of the current array, and then selectively flipping bits based on an alternating pattern in the third quarter of the array. This pattern is governed by the toggle variable, which depends on the value of k (the current level of recursion).
Special handling and manual adjustments are applied to certain entries in the arrays based on their indices and the value of k. This likely represents the behavior of the specific Turing machine you’re simulating.
Lastly, the code outputs a sequence of numbers, each of which is the sum of 2^k (for certain values of k) where the corresponding entry in the g[k] array is 1. This effectively translates the binary sequence into a sequence of integers, which could be the sequence you’re trying to generate.
Remember, while this agreement of 512k terms provides a strong consistency check for your Turing machine simulation, the behavior of the machine may still evolve in complex ways as the sequence continues. Make sure to carefully verify and test your code as you extend it further.
