A047474: Numbers that are congruent to {0, 2, 3} mod 8. 

Constant, high-pitched sound with a pure tone. 

Residue counts:
2   [250000, 125000]
3   [125000, 124999, 125001]
4   [125000, 0, 125000, 125000]
5   [75000, 75000, 75000, 75000, 75000]
6   [83333, 41666, 83334, 41667, 83333, 41667]
7   [53572, 53571, 53572, 53572, 53571, 53571, 53571]
8   [125000, 0, 125000, 125000, 0, 0, 0, 0]
9   [41667, 41666, 41667, 41666, 41666, 41667, 41667, 41667, 41667]
10   [50000, 25000, 50000, 25000, 50000, 25000, 50000, 25000, 50000, 25000]
11   [34091, 34090, 34092, 34090, 34091, 34091, 34090, 34092, 34091, 34090, 34092]
12   [41667, 0, 41667, 41667, 41666, 0, 41666, 41666, 41667, 0, 41667, 41667]

First 100 first differences:
[1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 
2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 
2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 
2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1, 5, 2, 1]

Exactly 3/8 of the terms less than 10^6 are in the sequence, giving it an essentially constant density.

In the spectrogram, there are spectral lines at approximately all multiples of 44100/8 hz. 

The waveform is periodic. 

For mod 8, the distribution is directly connected to the sequence, so the residue 
classes besides 0, 2, and 3 have 0 terms in them. For mod 4, the terms are uniformly 
distributed across residues 0, 2, and 3, while residue 1 has 0 terms. This happens 
because 0 mod 8 becomes 0 mod 4, 2 mod 8 becomes 2 mod 4, and 3 mod 8 becomes 3 mod 4, 
since 4 is a factor of 8. Thus, residue 1 mod 4 is the only residue class that is never 
produced. The value 8/3 is still related to the mod 8 pattern. Since the sequence contains 
3 allowed residue classes in each block of 8 numbers, the sound has a repeated pattern 
with 3 hits every 8 samples. Additionally, for mod 12, residues 1, 5, and 9 have 0 terms. 
This happens because any number congruent to 1, 5, or 9 mod 12 is always congruent to 
either 1 or 5 mod 8. Since residues 1 and 5 mod 8 are not allowed by the sequence restriction, 
residues 1, 5, and 9 mod 12 do not appear.

The sequence is infinite because all multiples of 8 are in the sequence.

-- Lauren Yee