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Forum: Analysis & Analytic Number Theory

2016-09-08, 14:03

Replies: 24

from i to π

Views: 14,177

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

from i to π

Views: 14,177

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

from i to π

Views: 14,177

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

from i to π

Views: 14,177

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

from i to π

Views: 14,177

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

from i to π

Views: 14,177

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

from i to π

Views: 14,177

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...

Showing results 1 to 7 of 7

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