WXML Autumn 2018

Number Theory and Noise

Joo Young "Jon" Kim, Erik Huang, Pooja Ramanathan

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

OIES id description sound player download creator quarter tags comments
A000069 Odious numbers: numbers with an odd number of 1's in their binary expansion.

00:00/00:00
download Erik Huang Aut2018
A000290 The squares

00:00/00:00
download Erik Huang Aut2018
A000567 Octagonal numbers: n*(3*n-2). Also called star numbers.

00:00/00:00
download Erik Huang Aut2018
A000959 Lucky numbers

00:00/00:00
download Erik Huang Aut2018
A001105 a(n) = 2*n^2.

00:00/00:00
download Erik Huang Aut2018
A001964 Wythoff game.

00:00/00:00
download Erik Huang Aut2018
A002061 Central polygonal numbers: a(n) = n^2 - n + 1.

00:00/00:00
download Erik Huang Aut2018
A002113 Palindromes in base 10.

00:00/00:00
download Erik Huang Aut2018
A002808 The composite numbers: numbers n of the form x*y for x > 1 and y > 1.

00:00/00:00
download Erik Huang Aut2018
A006753 Smith numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity).

00:00/00:00
download Erik Huang Aut2018
A006995 Binary palindromes: numbers whose binary expansion is palindromic.

00:00/00:00
download Erik Huang Aut2018
A007602 Numbers that are divisible by the product of their digits.

00:00/00:00
download Erik Huang Aut2018
A007623 Integers written in factorial base.

00:00/00:00
download Erik Huang Aut2018
A007770 Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map includes 1.

00:00/00:00
download Erik Huang Aut2018
A010784 Numbers with distinct decimal digits.

00:00/00:00
download Erik Huang Aut2018
A014190 Palindromes in base 3 (written in base 10).

00:00/00:00
download Erik Huang Aut2018
A014192 Palindromes in base 4 (written in base 10).

00:00/00:00
download Erik Huang Aut2018
A014486 List of totally balanced sequences of 2n binary digits written in base 10. Binary expansion of each term contains n 0's and n 1's and reading from left to right (the most significant to the least significant bit), the number of 0's never exceeds the number of 1's.

00:00/00:00
download Erik Huang Aut2018
A018252 The nonprime numbers (1 together with the composite numbers).

00:00/00:00
download Erik Huang Aut2018
A029803 Numbers that are palindromic in base 8.

00:00/00:00
download Erik Huang Aut2018
A029952 Palindromic in base 5.

00:00/00:00
download Erik Huang Aut2018
A029953 Palindromic in base 6.

00:00/00:00
download Erik Huang Aut2018
A029954 Palindromic in base 7.

00:00/00:00
download Erik Huang Aut2018
A029955 Palindromic in base 9.

00:00/00:00
download Erik Huang Aut2018
A050224 1/2-Smith numbers.

00:00/00:00
download Erik Huang Aut2018
A052223 Numbers whose sum of digits is 9.

00:00/00:00
download Erik Huang Aut2018
A072543 Numbers whose largest decimal digit is also the initial digit (to 107)

00:00/00:00
download Erik Huang Aut2018
A104390 2-Smith numbers.

00:00/00:00
download Erik Huang Aut2018
A139250 Toothpick sequence.

00:00/00:00
download Erik Huang Aut2018
A153880 Shift factorial base representation left by one digit (to 4 million)

00:00/00:00
download Erik Huang Aut2018
A166459 Numbers whose sum of digits is 19.

00:00/00:00
download Erik Huang Aut2018
A235151 Numbers whose sum of digits is 12.

00:00/00:00
download Erik Huang Aut2018
A235229 Numbers whose sum of digits is 20.

00:00/00:00
download Erik Huang Aut2018
A243615 Numbers n whose digital sum equals the number of binary digits in its binary expansion.

00:00/00:00
download Erik Huang Aut2018
A243617 Numbers n whose sum of digits equals the number of bits in its binary expansion. No zeros allowed in the digital expansion.

00:00/00:00
download Erik Huang Aut2018
A001358 Semiprimes

00:00/00:00
download Pooja Ramathan Aut2018
A003622 The Wythoff compound sequence AA: [n*phi^2] - 1, where phi = (1+sqrt(5))/2.

00:00/00:00
download Pooja Ramathan Aut2018 beatty
A004678 Primes written in base 4.

00:00/00:00
download Pooja Ramathan Aut2018
A004680 Primes written in base 6.

00:00/00:00
download Pooja Ramathan Aut2018
A004754 Numbers whose binary expansion starts 10.

00:00/00:00
download Pooja Ramathan Aut2018
A004758 Binary expansion starts 110.

00:00/00:00
download Pooja Ramathan Aut2018
A005728 Number of fractions in Farey series of order n.

00:00/00:00
download Pooja Ramathan Aut2018
A005891 Centered pentagonal numbers: (5n^2+5n+2)/2.

00:00/00:00
download Pooja Ramathan Aut2018
A005994 Alkane (or paraffin) numbers l(7,n).

00:00/00:00
download Pooja Ramathan Aut2018
A100484 Even semiprimes

00:00/00:00
download Pooja Ramathan Aut2018
A112393 Semiprimes n such that 3*n - 2 is a square.

00:00/00:00
download Pooja Ramathan Aut2018
A242756 Semiprimes having only the curved digits.

00:00/00:00
download Pooja Ramathan Aut2018
A277093 Numbers k such that sin(k) > 0 and sin(k+2) > 0.

00:00/00:00
download Pooja Ramathan Aut2018
Approximation of A277093 based on difference pattern [6,6,6,7,6,6,6,1]

00:00/00:00
download Pooja Ramathan Aut2018
Approximation of A277093 based on difference pattern [6,6,6,7,6,6,6,1,6,6,6,7,6,6,6,1,6,6,6,7,6,6,6,1,6,6,6,7,6,6,6,1,6,6,6,7,6,6,6,1,6,6,6,7,6,6,6,1,6,6,6,7,6,6,6,1,6,6,6,7]

00:00/00:00
download Pooja Ramathan Aut2018
A277094 Numbers k such that sin(k) > 0 and sin(k+2) < 0.

00:00/00:00
download Pooja Ramathan Aut2018
A277095 Numbers k such that sin(k) < 0 and sin(k+2) > 0.

00:00/00:00
download Pooja Ramathan Aut2018
A277096 Numbers k such that sin(k) < 0 and sin(k+2) < 0.

00:00/00:00
download Pooja Ramathan Aut2018
Numbers n congruent to 0 mod 1000.

00:00/00:00
download Joo Young "Jon" Kim Aut2018
Numbers n congruent to 1 mod 1000.

00:00/00:00
download Joo Young "Jon" Kim Aut2018
Numbers n congruent to 479 mod 1000.

00:00/00:00
download Joo Young "Jon" Kim Aut2018
Numbers congurnet to 0 or n mod 30, with n running from 0 to 30, increasing each second.

00:00/00:00
download Joo Young "Jon" Kim Aut2018

back to main project page