A257222: Numbers that have at least one divisor containing the digit 5 in base 10.

Rhythmic with groups of beats followed varying lengths of pauses.

Residue counts:
2   [455820, 362678]
3   [296334, 261045, 261119]
4   [238838, 181153, 216982, 181525]
5   [200000, 154531, 154306, 155031, 154630]
6   [160767, 113516, 147524, 135567, 147529, 113595]
7   [128428, 115027, 114985, 115087, 114980, 115016, 114975]
8   [122132, 90009, 108424, 90654, 116706, 91144, 108558, 90871]
9   [102104, 87043, 87009, 97087, 86938, 87038, 97143, 87064, 87072]
10   [100000, 66436, 88514, 65353, 89533, 100000, 88095, 65792, 89678, 65097]
11   [81251, 73707, 73741, 73759, 73801, 73739, 73703, 73677, 73737, 73700, 73683]
12   [82228, 56680, 69202, 67779, 78288, 56685, 78539, 56836, 78322, 67788, 69241, 56910]

Density information:
A(x) at x=10,100,1000,...:
[2, 28, 470, 6306, 74211, 818498]

A(x)/x at x=10,100,1000,...:
0.2,0.28,0.47,0.6306,0.74211,0.818498,

First 100 first differences:
[5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 
 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
 1, 2, 3, 3, 2, 1, 3, 1, 2, 3, 5, 5, 5, 5, 4, 1, 3, 2, 2, 3, 1, 4, 4, 1, 3, 2, 2, 
 3, 1, 4, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5]

First 99 second differences:
[0,0,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,-3,0,-1,0,1,0,0,0,-1,0,1,0,
 3,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,1,1,0,-1,-1,2,-2,1,1,2,0,0,0,-1,-3,2,-1,0,1,-2,
 3,0,-3,2,-1,0,1,-2,3,1,0,-4,0,0,0,0,0,0,0,0,0,4,0,0,0]

There are strong frequency lines at 8820Hz and 11025Hz, corresponding to 44100/5
and 44100/4, respectively. Weaker frequency lines exist at 4410Hz and 14700Hz
corresponding to 44100/10 and 44100/3. There is significantly more elements
in the sequence that are congruent to 0 mod 5 due to any number being divisible
by 5 being in the sequence. Similarly, there are more elements that are 
congruent to 0 or 5 mod 10.


-- David Oh