A074851: Numbers k such that k and k+1 both have exactly 2 distinct prime factors.

Harsh static noise.

Residue counts:
2   [31216, 31189]
3   [11148, 40156, 11101]
4   [16724, 14513, 14492, 16676]
5   [3853, 18210, 18276, 18202, 3864]
6   [50, 20039, 11049, 11098, 20117, 52]
7   [2411, 11541, 11492, 11472, 11581, 11526, 2382]
8   [8977, 7256, 7285, 7710, 7747, 7257, 7207, 8966]
9   [4213, 13346, 3498, 3478, 13449, 3446, 3457, 13361, 4157]
10   [32, 9027, 9066, 9101, 3834, 3821, 9183, 9210, 9101, 30]
11   [1378, 6631, 6627, 6618, 6671, 6585, 6553, 6669, 6623, 6651, 1399]
12   [46, 9322, 5148, 5912, 10777, 5, 4, 10717, 5901, 5186, 9340, 47]

Density information:
A(x) at x=10,100,1000,...:
[0, 31, 266, 1554, 9255, 62405]

A(x)/x at x=10,100,1000,...:
0.0,0.31,0.266,0.1554,0.09255,0.062405,

First 100 first differences:
[6, 1, 12, 1, 1, 3, 1, 5, 1, 5, 1, 3, 1, 1, 1, 5, 6, 6, 1, 1, 9, 1, 1, 4, 
 1, 1, 1, 1, 3, 1, 12, 4, 1, 1, 1, 4, 1, 10, 1, 1, 6, 1, 1, 1, 1, 1, 1, 5, 
 6, 1, 1, 1, 10, 4, 1, 1, 6, 1, 3, 1, 12, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 
 1, 1, 6, 1, 10, 1, 8, 3, 1, 1, 4, 8, 6, 7, 4, 9, 4, 4, 1, 1, 1, 3, 1, 1, 1, 
 15, 1, 3]

First 99 second differences:
[-5,11,-11,0,2,-2,4,-4,4,-4,2,-2,0,0,4,1,0,-5,0,8,-8,0,3,-3,0,0,0,2,-2,11,
 -8,-3,0,0,3,-3,9,-9,0,5,-5,0,0,0,0,0,4,1,-5,0,0,9,-6,-3,0,5,-5,2,-2,11,-11,
 0,2,-2,0,0,3,-3,0,0,0,0,0,5,-5,9,-9,7,-5,-2,0,3,4,-2,1,-3,5,-5,0,-3,0,0,2,-2,
 0,0,14,-14,2]

On the spectrogram, 3 lines stand out which are at 6300Hz, 7350Hz and 8820Hz.
These corresond to 44100/7, 44100/6, and 44100/5. There are very few numbers 
congruent to 0 mod 6 since any number divisible by 6 is divisible 2 and 3 which
are 2 distinct prime factors. As such, we can only have numbers that are the product
of some power of 2 multiplied with some power of 3 that are congruent to 0 mod 6
in the sequence. A similar thing holds for 5 mod 6, as k + 1 must be congruent to 0
mod 6. Similarly, there are very few integers that are congruent to 0 and 9 mod 10. 


--David Oh