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.

description | sound player | creator | ||

rational convergents toward sqrt(2) Beatty sequence | download | Emily Flanagan | ||

composites with progressively increasing maximal prime factor (2-19), then all composites | download | Penny Espinoza |

OIES id | description | sound player | creator | |

A184774 | primes of the form floor(k*sqrt(2)) | download | Emily Flanagan | |

A184775 | numbers n such that floor(n*sqrt(2)) is prime | download | Emily Flanagan | |

A184777 | primes of the form 2k + floor(k*sqrt(2)) | download | Emily Flanagan | |

A184778 | numbers n such that 2n+floor(n*sqrt(2)) is prime | download | Emily Flanagan | |

A002984 | a(0) = 1; for n>0, a(n) = a(n-1) + floor( sqrt a(n-1) ) | download | Emily Flanagan | |

A013929 | non-squarefree numbers | download | Emily Flanagan | |

A017533 | number of the form 12n+1 | download | Emily Flanagan | |

A158708 | primes p such that p + floor(p/2) is prime | download | Emily Flanagan | |

A158709 | primes p such that p + ceiling(p/2) is prime | download | Emily Flanagan | |

A168363 | squares and cubes of primes | download | Emily Flanagan | |

A175914 | primes p such that p+2*q is prime, where q is the prime after p | download | Emily Flanagan | |

A000093 | a(n) = floor(n^(3/2)). | download | Emily Flanagan | |

A000212 | a(n) = floor(n^2/3) | download | Emily Flanagan | |

A001952 | a Beatty sequence: a(n) = floor(n*(2 + sqrt(2))) | download | Emily Flanagan | |

A002620 | quarter-squares: floor(n/2)*ceiling(n/2), equivalently, floor(n^2/4) | download | Emily Flanagan | |

A003154 | centered 12-gonal numbers (also star numbers: 6*n*(n-1) + 1). | download | Emily Flanagan | |

A007590 | floor(n^2/2) | download | Emily Flanagan | |

A014657 | numbers n that divide 2^k + 1 for some k | download | Emily Flanagan | |

A032528 | concentric hexagonal numbers: floor( 3*n^2 / 2 ) | download | Emily Flanagan | |

A033581 | a(n) = 6*n^2 | download | Emily Flanagan | |

A035336 | a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2 | download | Emily Flanagan | |

A072065 | numbers of the form 12n+k, where k=0, 2, 9, or 11 | download | Penny Espinoza | |

A000040 | the primes, starting from 1 | download | Penny Espinoza | |

A000040 | the primes, starting from 10^{7} | download | Penny Espinoza | |

A000040 | the primes, starting from 10^{8} | download | Penny Espinoza | |

A000040 | the primes, starting from 10^{9} | download | Penny Espinoza | |

A000040 | the primes, starting from 10^{10} | download | Penny Espinoza | |

A000040 | the primes, starting from 10^{11} | download | Penny Espinoza | |

A000040 | the primes, starting from 10^{12} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{10} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{20} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{30} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{40} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{100} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{200} | download | Penny Espinoza | |

A000040 | primes, starting at 10^{400} | download | Penny Espinoza | |

A077800 | twin primes, starting at 10^{10} | download | Penny Espinoza | |

A077800 | twin primes, starting at 10^{30} | download | Penny Espinoza | |

A077800 | twin primes, starting at 10^{100} | download | Penny Espinoza | |

A050504 | floor of n log n | download | Hannah Claire Van Wyk | |

floor of n^1.01 | download | Hannah Claire Van Wyk |

- Spectrogram for A050504 and floor of n^1.01
- Spectrogram for A014657
- Spectrogram for A158709
- Spectrogram for A158708
- Spectrogram for A168363
- Spectrogram for A017533
- Spectrogram for A013929
- Spectrogram for A002984
- Spectrogram for A007661
- Spectrogram for sqrt 2 convergents
- Waveform for A032924 - 0 to 23 seconds
- Waveform for A032924 - 2 to 4 seconds
- Waveform for A032924 - 2 to 2.7 seconds
- Waveform for A032924 - 2 to 2.3 seconds
- Waveform for A032924 - 2 to 2.1 seconds
- Waveform for A032924 - 2 to 2.04 seconds
- Waveform for A032924 - 2 to 2.02 seconds
- Waveform for A005823 - 0 to 23 seconds
- Waveform for A005823 - 2.5 to 4.1 seconds
- Waveform for A005823 - 2.6 to 3.2 seconds
- Waveform for A005823 -2.67 to 2.83 seconds
- Waveform for A005823 - 2.67 to 2.73 seconds
- Waveform for A005823 - 2.677 to 2.695 seconds
- Waveform for A005823 - 2.677 to 2.684 seconds
- Frequency analysis - twin primes - 10
^{200}seconds - Frequency analysis - twin primes - 10
^{300}seconds - Frequency analysis - twin primes - 10
^{400}seconds - Frequency analysis - twin primes - 10
^{500}seconds - Frequency analysis - primes - 10
^{0}seconds - Frequency analysis - primes - 10
^{600}seconds