A156666: Primes where the last digit is greater than any other digit.

Rhythmic and repetitive. Groups of 9 "beats" separated by brief pauses. As
the sound goes farther out, there are longer pauses.

Residue counts:
2   [0, 109743]
3   [0, 54827, 54916]
4   [0, 58433, 0, 51310]
5   [0, 0, 20312, 149, 89282]
6   [0, 54827, 0, 0, 0, 54916]
7   [0, 18284, 18274, 18213, 18304, 18308, 18360]
8   [0, 29949, 0, 25737, 0, 28484, 0, 25573]
9   [0, 18275, 18269, 0, 18308, 18365, 0, 18244, 18282]
10   [0, 0, 0, 149, 0, 0, 0, 20312, 0, 89282]
11   [0, 10907, 10984, 10977, 11020, 11033, 10945, 10953, 11014, 10976, 10934]
12   [0, 29162, 0, 0, 0, 29271, 0, 25665, 0, 0, 0, 25645]


Density information:
A(x) at x=10,100,1000,...:
[0, 11, 61, 359, 2238, 15198, 109743]

A(x)/x at x=10,100,1000,...:
0.0,0.11,0.061,0.0359,0.02238,0.015198,0.0109743

First 100 first differences:
[4, 2, 4, 6, 8, 10, 12, 8, 12, 10, 14, 4, 2, 4, 14, 10, 2, 10, 8, 10, 
 12, 44, 4, 2, 10, 18, 12, 38, 10, 20, 10, 2, 10, 8, 12, 10, 20, 10, 
 20, 10, 8, 10, 12, 30, 38, 10, 12, 38, 10, 2, 28, 12, 50, 10, 20, 30, 
 40, 20, 10, 20, 150, 4, 6, 20, 10, 20, 34, 6, 8, 6, 6, 84, 4, 6, 6, 
 8, 12, 10, 20, 10, 18, 12, 8, 40, 42, 18, 2, 10, 8, 12, 30, 60, 10, 
 8, 12, 28, 2, 10, 8, 10]

First 99 second differences:
[-2,2,2,2,2,2,-4,4,-2,4,-10,-2,2,10,-4,-8,8,-2,2,2,32,-40,-2,8,8,-6,
 26,-28,10,-10,-8,8,-2,4,-2,10,-10,10,-10,-2,2,2,18,8,-28,2,26,-28,-8,
 26,-16,38,-40,10,10,10,-20,-10,10,130,-146,2,14,-10,10,14,-28,2,-2,0,
 78,-80,2,0,2,4,-2,10,-10,8,-6,-4,32,2,-24,-16,8,-2,4,18,30,-50,-2,4,16,
 -26,8,-2,2]

Most prominent line at 4410Hz which corresponds to 44100/10. 10 is important
to this sequence due to the sequence being based on digits. The last digit
of any number in the sequence can only be congruent to 1, 3, 7, or 9 due to 
the primes. The requirement that the last digit is greater than any other digit
results in there being no numbers congruent to 1 mod 10. Then, there are very
few primes where 3 is the greatest digit as the only other digits that can be in
the number are 0, 1, or 2. As a result, we see that the majority of numbers
in the sequence are congruent to 7 or 9 mod 10.


--David Oh