>>8823 nice work AA
Can see a' growth of +4 / t for both the e & f.
Have you done anything in negative t space?
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thinking about what an a'[0] or a'[-1] might be for the (e,1).
Will try and work a bit this eve as well. Been quite the day already.
Looked briefly at the: Pythagorean Primes Series (q)
Patterns didn't particularly jump out, but here's the output for q=5 up to q=123214686833351935572985 (which is up to prime value of 113 in the list):
https://pastebin.com/PEa37Snx
Was looking more at the '11' ending bits for the binary output of the Pythagorean Primes. Noted this was a pattern congruent to 1 mod(4).
Reading up on them a bit more (simply https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares)
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as:
p=x^2 +y^2, with with x and y integers, if and only if p is congruent to 1 (mod 4).
The prime numbers for which this is true are called Pythagorean primes. For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways:
5= 1^2 + 2^2, 13= 2^2 + 3^2, 17= 1^2 + 4^2, 29= 2^2 + 5^2, 37= 1^2 + 6^2, 41=4^2 + 5^2
The flip-side (column 2!), is that:
the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 or 1 modulo 4.
And a cap of the Julia Set, got this working the other day a bit differently.