A156666-all: Integers where the last digit is greater than any other digit.

Sounds similar to A156666, being rhythmic with short pauses between
groups of beats. More high-pitched compared to A156666.

Residue counts:
2   [312956, 665440]
3   [326130, 326133, 326133]
4   [156478, 355282, 156478, 310158]
5   [15624, 46655, 117711, 262871, 535535]
6   [104318, 221814, 104319, 221812, 104319, 221814]
7   [139770, 139771, 139771, 139771, 139771, 139771, 139771]
8   [78239, 181769, 78239, 155079, 78239, 173513, 78239, 155079]
9   [108710, 108711, 108711, 108710, 108711, 108711, 108710, 108711, 108711]
10   [0, 0, 63, 728, 4095, 15624, 46655, 117648, 262143, 531440]
11   [87986, 88150, 88570, 89095, 89560, 89830, 89830, 89560, 89095, 88570, 88150]
12   [52160, 118428, 52160, 103385, 52159, 118427, 52158, 103386, 52159, 118427, 52160, 103387]

Density information:
A(x) at x=10,100,1000,...:
[0, 36, 276, 2016, 15324, 120816, 978396]

A(x)/x at x=10,100,1000,...:
0.0,0.36,0.276,0.2016,0.15324,0.120816,0.0978396,

First 100 first differences:
[1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 
 1, 6, 1, 1, 1, 1, 7, 1, 1, 1, 8, 1, 1, 9, 1, 10, 13, 1, 
 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 
 1, 5, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 7, 1, 1, 1, 8, 1, 1, 9, 
 1, 10, 14, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 
 1, 1, 1]

First 99 second differences:
[0,0,0,0,0,0,3,-3,0,0,0,0,0,4,-4,0,0,0,0,5,-5,0,0,0,6,-6,0,0,
 7,-7,0,8,-8,9,3,-12,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,3,-3,0,0,0,0,
 0,4,-4,0,0,0,0,5,-5,0,0,0,6,-6,0,0,7,-7,0,8,-8,9,4,-13,0,0,0,0,0,
 3,-3,0,0,0,0,0,3,-3,0,0,0,0,0]

The spectrogram has lines at 4410Hz and 8820Hz which correspond to
44100/10 and 44100/5. We see that there are no numbers in the sequence
that are congruent to 0 nor 1 mod 10 due to the requirement that 
the last digit has to be greater than any other digit. As numbers that 
end in a larger number are more capable of having that last digit be 
greater than any other digit, the quantity of numbers mod 10 increases from
left to right.


--David Oh