My favorite integer sequence

[sheldonison]

How large a value of "k" have you calculated A(k) for, and how long does it take? ....
Then I took the inverse of the zerocount function at 16, 15.5, 15, 14.5. 14, 13.5, 13, 12.5 and averaged all of the alpha_1 values with a binomial weighting.... could try more terms though since I'm only using k=800000

I need to take a look at your acceleration trick, because it's remarkably accurate, for only going up to about 2^20 terms. I've taken my calculations out to 2^432 terms so far, and I'm only getting a couple more digits than you are, using simple quadratic interpolation.

I downloaded your memory efficient code, jdf_seq_v2.gp, and it works great I figured out how to initialize the SeqParts array for a power of 2, and then it is fast for numbers not to much bigger than that exact power of 2. What is the algorithm for initialization halfway to the next power of 2? For example (2^24+2^23)? I don't understand the polynomials well enough to write my own SeqPowers2 initialization starting with 3,6,12,24....