Potential new "Gap" sequence in a similar style to A382482

[Sam Khan]

Hi All,

There was a bit of controversy when I submitted A382482, in that it was considered a bit too arbitrary. I've come up with another with slightly more arbitrary rules that I won't go into right now. But didn't know if it might be worth submitting based on the interesting, almost fractal-like graphs generated. What do you think of the below - each graph has interesting lines leaning slightly to the left that appear to remain even when zooming out to 700,000 terms?

Cheers

Sameer

[mi...@vincico.com]

Sam,

 

I don’t think A382482 is “arbitrary.” It seems to only employ indices and though the terms are not computed sequentially, the sequence is close to first principles and thereby seems interesting. Going to try to code it later today or tomorrow. [Edit: I coded it, it is keyword easy.]

 

Though I can’t point to similar sequences at the moment, there are sequences computed out of order but result in a well-defined integer sequence. (This, given only a few moments looking at it.)

 

Those are interesting scatterplots.

 

Best regards,

Mike

 

Cheers

 

Sameer

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[Sam Khan]

Thanks Mike 

Yes, I coded A382482 in Python, and then someone else did it in a much more efficient manner.

Maybe I will submit the new idea and see what people think. It took hours to run 700,000 terms, I imagine someone will code that more efficiently too! 

Sameer

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[Alex Violette]

Hey Sam,
I have a question about your graphs, did you make them in Google Sheets? If so, then I wonder how the 700k graph effects(or effected) your browser having all those terms loaded in for the graph on that sheet. I know it starts to lag once you get to a certain point.

Regards,
Alex Violette

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[Sam Khan]

Hi Alex 

Yes it was Google Sheets, and you are correct. It was very slow. The graph takes about 15 seconds to load, and the same amount of time anytime I try to change anything on it. I don't have Excel on my home computer! 

Sameer

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Sam