A023241  Primes that remain prime through 2 iterations of function f(x) = x + 6:

Sequence is quite sparse with only 2900 terms less than 10^6.

This sound gets progressively more "choppy" as time goes on. 

The residue counts are:

2   [0, 2900]
3   [0, 1448, 1452]
4   [0, 1419, 0, 1481]
5   [1, 1429, 1470, 0, 0]
6   [0, 1448, 0, 0, 0, 1452]
7   [1, 0, 0, 733, 713, 731, 722]
8   [0, 697, 0, 735, 0, 722, 0, 746]
9   [0, 489, 454, 0, 487, 520, 0, 472, 478]
10   [0, 1429, 0, 0, 0, 1, 0, 1470, 0, 0]
11   [1, 395, 350, 361, 344, 1, 358, 375, 353, 362, 0]
12   [0, 707, 0, 0, 0, 712, 0, 741, 0, 0, 0, 740]

In the spectrogram, there are four horizontal spectral lines that are prominently visible. These lines lie at about 1470 (44100/30) Hz, 2520 (44100/17.5) Hz, 8820 (44100/5) Hz, and 13370 (about 44100/3.3) Hz. 

There is quite a bit of non-conformity throughout the different moduli. 
There are no terms (or just one term) congruent to 3 modulo 5, 1 modulo 7, 2 modulo 7, 3 modulo 10, 9 modulo 9, 5 modulo 11, 10 modulo 11; these are residue classes in which infinitely many primes fall.

But the ones that show up the boldest in the spectrogram is at moduli 5 and 30. 

It is also worth noting that the plot spectrum shows that as the frequency gets higher, the decibel about becomes sinusoidal with troughs at about 3340 Hz, 11110 Hz, and 18750 Hz.  It is not clear if this is an 
anomaly of the spectrum plotting algorithm as a result of the extreme sparseness of the sequence or if this really
is a spectral feature of the sequence.