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Search: Posts Made By: CRGreathouse
Forum: Analysis & Analytic Number Theory 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.
Forum: Analysis & Analytic Number Theory 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...
Forum: Analysis & Analytic Number Theory 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....
Forum: Analysis & Analytic Number Theory 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.
Forum: Analysis & Analytic Number Theory 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
Forum: Analysis & Analytic Number Theory 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
Forum: Analysis & Analytic Number Theory 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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