A033298: a(n+1) = a(n) + sum of digits of a(n)^2, with a(1) = 1.

High-pitched and fast.

Moves into a constant echoing sound that dies out and then repeats
along with a continuous static noise behind it that continues
throughout.

Residue counts:
2   [9969, 10031]
3   [19998, 1, 1]
4   [4919, 5013, 5050, 5018]
5   [4927, 4941, 3821, 2960, 3351]
6   [9968, 1, 1, 10030, 0, 0]
7   [2833, 2839, 2809, 2804, 2948, 2905, 2862]
8   [2458, 2541, 2534, 2515, 2461, 2472, 2516, 2503]
9   [0, 1, 1, 0, 0, 0, 19998, 0, 0]
10   [2630, 2238, 1580, 1374, 1470, 2297, 2703, 2241, 1586, 1881]
11   [1804, 1852, 1826, 1781, 1843, 1855, 1829, 1858, 1834, 1765, 1753]
12   [4919, 1, 1, 5018, 0, 0, 5049, 0, 0, 5012, 0, 0]


First 100 first differences:
[1, 4, 9, 9, 18, 18, 9, 18, 27, 27, 27, 18, 27, 27, 18, 27, 18, 27, 18, 
 9, 27, 27, 27, 27, 18, 27, 9, 27, 27, 27, 9, 27, 27, 36, 27, 27, 27, 
 18, 27, 27, 27, 27, 27, 36, 36, 9, 27, 27, 18, 36, 36, 27, 18, 27, 18, 
 27, 27, 27, 27, 36, 36, 27, 18, 36, 27, 36, 27, 27, 36, 27, 27, 36, 27, 
 27, 27, 45, 36, 36, 18, 27, 27, 36, 27, 27, 27, 27, 36, 36, 27, 18, 27, 
 18, 36, 45, 27, 36, 27, 18, 36, 36]

First 99 second differences:
[3,5,0,9,0,-9,9,9,0,0,-9,9,0,-9,9,-9,9,-9,-9,18,0,0,0,-9,9,-18,18,0,0,-18,
 18,0,9,-9,0,0,-9,9,0,0,0,0,9,0,-27,18,0,-9,18,0,-9,-9,9,-9,9,0,0,0,9,0,-9,
 -9,18,-9,9,-9,0,9,-9,0,9,-9,0,0,18,-9,0,-18,9,0,9,-9,0,0,0,9,0,-9,-9,9,-9,
 18,9,-18,9,-9,-9,18,0]

There are four prominent lines along in the spectrogram for this sequence.
The lines correspond to about 4900Hz, 9800Hz, 14700Hz, and 19600Hz.
The shape of the frequency plot is interesting in that the frequencies 
just around the prominent lines are much less prominent than other frequencies.


-- David Oh