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This just shows the reduced residues mod n. There are n squares in the nth row from the top. Color the kth square of the nth row black if gcd(k,n)=1, color it r
by mathythrowaway 8y ago
This just shows the reduced residues mod n. There are n squares in the nth row from the top. Color the kth square of the nth row black if gcd(k,n)=1, color it red otherwise.
- tgb 8y agoThat's what the OEIS sequence they link to says. I hadn't realized that it makes such a beautiful pattern!
- gowld 8y agoHow is that? Isn't it plotting a prime spiral, not GCD? Obviously prime implies gcd=1, but the "kth" square isn't "k", because it's a spiral counting up from the center.
- mathythrowaway 8y agoNo, it isn't plotting a prime spiral. Each square in their triangle is a block of 75 numbers. Within the nth row the numbers are sorted by residue mod n.
- chickenstrips 8y agoYou're correct. The correspondence just seems to be due to some bound on the prime gap for arithmetic progressions (or perhaps something even more trivial that I'm missing). A cursory search suggests it might be a consequence of Ingham's bound. In any case, it doesn't yield much of interest.