A123608

This sequence's sound is very noisy, quite similar to the primes sound.

Looking at the sequence's distribution modulo 6, we see these counts for
terms up to 10^6:
[98004, 127435, 129431, 129435, 127402, 97862]
So we see the terms of the sequence are more likely to be congruent to 1, 2, 3, or 4
mod 6 than 0 or 5.

If we look at what k, k+1 and 2k+1 are modulo 6, we see the following
   k 0 1 2 3 4 5 
k+1  1 2 3 4 5 0
2k+1 1 3 5 1 3 5

From this we see that if k is not congruent to 0 or 5 mod 6, then 
two of k, k+1, 2k+1 are necessarily composite.
On the other hand, if k is congruent to 0 or 5 mod 6, we may
only conclude that one of k, k+1, 2k+1 is necessarily composite.

So, this suggest that more terms of the sequence should fall into 
the residue classes 1, 2, 3, 4 mod 6 than into 0 or 5.

This non-uniformity modulo 6 is reflected in a strong spectral line in the sound at 
approximately 7350=44100/6 hz.

-- M. Conroy