A059094: Numbers whose sum of digits is a cube.

Repetitive, very high-pitched.


Residue counts:
2   [28423, 28123]
3   [55252, 7, 1287]
4   [14237, 14092, 14186, 14031]
5   [11376, 11501, 11477, 11282, 10910]
6   [27626, 1, 791, 27626, 6, 496]
7   [8077, 8079, 8078, 8078, 8078, 8078, 8078]
8   [7125, 7053, 7096, 7019, 7112, 7039, 7090, 7012]
9   [55252, 7, 0, 0, 0, 0, 0, 0, 1287]
10   [5341, 5611, 5841, 6001, 6070, 6035, 5890, 5636, 5281, 4840]
11   [4275, 5765, 4531, 5608, 4921, 5311, 5311, 4921, 5608, 4531, 5764]
12   [13806, 1, 365, 13806, 5, 271, 13820, 0, 426, 13820, 1, 225]

Density information:
A(x) at x=10,100,1000,...:
[3, 12, 50, 390, 5341, 56546]

A(x)/x at x=10,100,1000,...:
0.3,0.12,0.05,0.039,0.05341,0.056546,

First 100 first differences:
[7, 2, 7, 9, 9, 9, 9, 9, 9, 9, 20, 7, 9, 9, 9, 9, 9, 9, 9, 36, 9, 9, 9, 9, 
 9, 9, 45, 9, 9, 9, 9, 9, 54, 9, 9, 9, 9, 63, 9, 9, 9, 72, 9, 9, 81, 9, 90, 
 199, 1, 7, 9, 9, 9, 9, 9, 9, 9, 36, 9, 9, 9, 9, 9, 9, 45, 9, 9, 9, 9, 9, 54, 
 9, 9, 9, 9, 63, 9, 9, 9, 72, 9, 9, 81, 9, 90, 199, 90, 9, 8, 9, 9, 9, 9, 9, 9, 
 45, 9, 9, 9, 9]

First 99 second differences:
[-5,5,2,0,0,0,0,0,0,11,-13,2,0,0,0,0,0,0,27,-27,0,0,0,0,0,36,-36,0,0,0,0,45,
 -45,0,0,0,54,-54,0,0,63,-63,0,72,-72,81,109,-198,6,2,0,0,0,0,0,0,27,-27,0,0,0,
 0,0,36,-36,0,0,0,0,45,-45,0,0,0,54,-54,0,0,63,-63,0,72,-72,81,109,-109,-81,-1,
 1,0,0,0,0,0,36,-36,0,0,0]

The spectrogram has lines at multiples of 44100/9 hz.
We can observe that the vast majority of numbers in the sequence are congruent to
0 mod 9 because the sequence includes every number whose digits add up to 27 and 
each of these numbers must be divisible by 9. 


-- David Oh