# Number Theory and Noise

## Mrigank Arora, Miranda Bugarin, Aanya Khaira

This project investigates the representations of sets of positive integers (sequences) as sound.

A digital audio waveform is created from a given set A of positive integers by setting sample number i to a non-zero constant c for all i in the set. All other samples are set to zero.

For example, the waveform for the primes starts like this: We use the standard CD-audio sampling rate of 44100 samples per second, so Δt = 1/44100= 0.0000226757... seconds.

For many sets, the result is what most people would describe as noise.

## OEIS sequences

A005101 Abundant numbers waveform built up from distinct subsequences. download Mrigank Arora Spr2019
A091191 Primitive abundant numbers: abundant numbers having no abundant proper divisor. download Mrigank Arora Spr2019
A028374 Curved numbers: numbers that only have curved digits (0,2,3,5,6,8,9) download Mrigank Arora Spr2019 digits
A034470 Prime numbers using only the curved digits (0,2,3,5,6,8,9) download Mrigank Arora Spr2019 digits
A192869 Thin primes: odd primes p such that p+1 is a prime (or 1) times a power of two. download Mrigank Arora Spr2019

A003234 Numbers n such that A003231(A001950(n)) = A001950(A003231(n)) - 1. download Miranda Bugarin Spr2019
A005384 Sophie Germain primes p: 2p+1 is also prime. download Miranda Bugarin Spr2019
A007640 Numbers k such that 2*k^2 - 2*k + 19 is composite. download Miranda Bugarin Spr2019
A055471 Divisible by the product of its nonzero digits. download Miranda Bugarin Spr2019 digits
A071204 Numbers which are multiples of their largest decimal digit. download Miranda Bugarin Spr2019 digits
A052382 Numbers without 0 as a base 10 digit, a.k.a. zeroless numbers. download Miranda Bugarin Spr2019 digits
A082943 Numbers without zero digits that are not divisible by any of their digits nor by the sum of their digits. download Miranda Bugarin Spr2019 digits
A031956 Numbers in which the number of distinct base 4 digits is 3. download Miranda Bugarin Spr2019 digits
A031957 Numbers in which the number of distinct base 5 digits is 3. download Miranda Bugarin Spr2019 digits
A031958 Numbers in which the number of distinct base 6 digits is 3. download Miranda Bugarin Spr2019 digits
A031959 Numbers in which the number of distinct base 7 digits is 3. download Miranda Bugarin Spr2019 digits
A031960 Numbers in which the number of distinct base 8 digits is 3. download Miranda Bugarin Spr2019 digits
A031961 Numbers in which the number of distinct base 9 digits is 3. download Miranda Bugarin Spr2019 digits
A031962 Numbers with exactly two distinct base 10 digits. download Miranda Bugarin Spr2019 digits
A031955 Numbers with exactly two distinct base 10 digits. download Miranda Bugarin Spr2019 digits
A101594 Numbers with exactly two distinct decimal digits, neither of which is 0. download Miranda Bugarin Spr2019 digits
A155107 Numbers n that are 23 or 30 (mod 53). download Miranda Bugarin Spr2019

A000404 Numbers that are the sum of 2 nonzero squares. download Aanya Khaira Spr2019
A000443 Numbers that are the sum of 2 squares in exactly 3 ways. download Aanya Khaira Spr2019
A025284 Numbers that are the sum of 2 nonzero squares in exactly 1 way. download Aanya Khaira Spr2019
A025285 Numbers that are the sum of 2 nonzero squares in exactly 2 ways. download Aanya Khaira Spr2019
A025286 Numbers that are the sum of 2 nonzero squares in exactly 3 ways. download Aanya Khaira Spr2019
A025287 Numbers that are the sum of 2 nonzero squares in exactly 4 ways. download Aanya Khaira Spr2019