A024508: Numbers that are a sum of 2 distinct nonzero squares in more than one way.

Sounds relatively high-pitched and consistently noisy throughout.

Residue counts:
2   [55554, 56401]
3   [11980, 49954, 50021]
4   [27463, 56401, 28091, 0]
5   [45906, 16520, 16501, 16501, 16527]
6   [5840, 25099, 24859, 6140, 24855, 25162]
7   [2032, 18327, 18332, 18297, 18326, 18339, 18302]
8   [13516, 28180, 28091, 0, 13947, 28221, 0, 0]
9   [11980, 16672, 16682, 0, 16645, 16649, 0, 16637, 16690]
10   [23625, 8544, 7974, 8524, 8002, 22281, 7976, 8527, 7977, 8525]
11   [769, 11124, 11099, 11123, 11095, 11093, 11129, 11140, 11141, 11137, 11105]
12   [2821, 25099, 12526, 0, 12309, 25162, 3019, 0, 12333, 6140, 12546, 0]

First 100 first differences:
[20, 40, 5, 15, 25, 15, 20, 16, 29, 10, 5, 25, 15, 20, 15, 25, 5, 7, 33, 15, 17, 
 3, 36, 4, 8, 7, 5, 15, 10, 3, 12, 20, 15, 5, 25, 15, 4, 21, 30, 5, 4, 8, 28, 5, 
 10, 5, 9, 11, 20, 8, 27, 25, 5, 15, 19, 6, 11, 4, 20, 24, 13, 3, 5, 15, 1, 14, 
 10, 15, 12, 3, 20, 6, 7, 17, 15, 20, 5, 15, 12, 3, 5, 5, 19, 16, 15, 21, 9, 8, 
 3, 24, 15, 5, 8, 12, 20, 15, 10, 8, 7, 9]

First 99 second differences:
[20,-35,10,10,-10,5,-4,13,-19,-5,20,-10,5,-5,10,-20,2,26,-18,2,-14,33,-32,4,-1,
 -2,10,-5,-7,9,8,-5,-10,20,-10,-11,17,9,-25,-1,4,20,-23,5,-5,4,2,9,-12,19,-2,-20,
 10,4,-13,5,-7,16,4,-11,-10,2,10,-14,13,-4,5,-3,-9,17,-14,1,10,-2,5,-15,10,-3,-9,
 2,0,14,-3,-1,6,-12,-1,-5,21,-9,-10,3,4,8,-5,-5,-2,-1,2]

The frequency has about 6 relatively prominent lines. The most prominent one is
at about 11250Hz, corresponding to 44100/4. Three other peaks are at about
5512.5Hz, 8820Hz, and 14700Hz which correspond to 44100/8, 44100/5, 44100/3, respectively.
The last two peaks are at 16500Hz and 18000Hz which divide 44100 into about 2.67 and 2.5.


--David Oh