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 Showing results 1 to 7 of 7 Search took 0.00 seconds. Search: Posts Made By: CRGreathouse
 2016-09-08, 14:03 Replies: 24 Views: 4,096 Posted By CRGreathouse If you're going to arbitrarily reject some values... If you're going to arbitrarily reject some values then you can adapt my method and see if it comes out as desired.
 2016-09-07, 21:11 Replies: 24 Views: 4,096 Posted By CRGreathouse Here's a heuristic suggesting that my constant is... Here's a heuristic suggesting that my constant is right. Start by looking at the circle with radius sqrt(x). All lattice points in the circle are (u, v) with u^2 + v^2 < x. The circle has area [$]\pi...  2016-09-07, 20:54 Replies: 24 Views: 4,096 Posted By CRGreathouse You left out 1^2 + 3^2 = 10 < 32. I think that... You left out 1^2 + 3^2 = 10 < 32. I think that when you correct your program it will count A008784 and you'll get the constant I had computed, 3/(4*Pi) = 0.2387324146378....  2016-09-06, 18:49 Replies: 24 Views: 4,096 Posted By CRGreathouse I think your program is trying to count A008784... I think your program is trying to count A008784 but it's buggy. It produces 5, 10, 17, 29, 34, 37, 41, 50, 58, 61, 65, 74, 85, 89, 97, 101, 122, 130 but not 13, 25, 26, etc.  2016-09-06, 17:04 Replies: 24 Views: 4,096 Posted By CRGreathouse For that I get n count up to 2^n 5 5 6 9 ... For that I get n count up to 2^n 5 5 6 9 7 18 8 33 9 66 10 125 11 240 12 461  2016-09-06, 16:53 Replies: 24 Views: 4,096 Posted By CRGreathouse Ah, you think he meant c^2 = u^2 + v^2 rather... Ah, you think he meant c^2 = u^2 + v^2 rather than c = u^2 + v^2? That doesn't match either, though: I get n count up to 2^n 5 10 6 25 7 59 8 126 9 273 10 582 11 1218  2016-09-06, 15:56 Replies: 24 Views: 4,096 Posted By CRGreathouse It sounds like you're guessing that the density... It sounds like you're guessing that the density of numbers [$]c=x^2+y^2[/$] with [$]\gcd(x,y)=1[/$] (A008784 (https://oeis.org/A008784)) is [$]1/(2\pi)[/\$] and you're asking why this is. But I...
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