My previous post managed to ensnare Ray Chandler into helping extend OEIS sequence A293355, which had reached term #384. Ray has access to "yafu" which allows him to factor large integers quickly. Sadly, I don't know how to get that program to run on my Mac. At any rate, thanks to Ray's persistent effort, he was able to extend the sequence past a local maximum at #398 and then down the other side to a point where the numbers were finally small enough that I could once again automate the procedure in Mathematica. The downslope reaches a local minimum at #923, then rises again, slowly and erratically:
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The ratios graph (that I had previously posted to term #384) extends now past term #3280:
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It clearly shows the differing "resonances" about which I had speculated.
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