login
Positive integers sorted by rote weight, rote quench and rote height.
1

%I #9 Mar 14 2015 00:25:47

%S 1,2,3,4,6,9,5,7,8,16,12,18,10,14,13,23,25,27,49,64,81,512,11,17,19,

%T 32,53,128,256,65536,36,26,46,50,54,98,125,162,2401,22,34,38,106,15,

%U 21,37,61,169,343,529,625,729,4096,19683,262144,29,41,43,83,97,103,121,227

%N Positive integers sorted by rote weight, rote quench and rote height.

%C For positive integer m, the rote weight in gammas is g(m) = A062537(m), the rote quench or primal code characteristic is q(m) = A108352(m) and the rote height in gammas is h(m) = A109301(m).

%C This sequence begins to differ from A113197 at the 40th term, a(40) = 22.

%H J. Awbrey, <a href="http://stderr.org/pipermail/inquiry/2005-October/003127.html">Table for Rote Weights 0 to 5</a>

%H J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>

%e Primal Functions, Primal Codes, Sort Parameters and Subtotals

%e ================================================================

%e Primal Function | ` ` ` Primal Code ` = ` a | g q h | r | s | t

%e ================================================================

%e { } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 1 0 | 1 | 1 | 1

%e ================================================================

%e 1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 0 1 | 1 | 1 | 1

%e ================================================================

%e 2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 2 2 | ` | ` |

%e 1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 2 2 | 2 | 2 | 2

%e ================================================================

%e 1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 0 2 | ` | ` |

%e 2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 0 2 | 2 | 2 |

%e ----------------+---------------------------+-------+---+---+---

%e 3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 2 3 | ` | ` |

%e 4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 2 3 | ` | ` |

%e 1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 2 3 | ` | ` |

%e 1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 2 3 | 4 | 4 | 6

%e ================================================================

%e 1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 0 2 | ` | ` |

%e 1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 0 2 | 2 | ` |

%e ----------------+---------------------------+-------+---+---+---

%e 1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 0 3 | ` | ` |

%e 1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 0 3 | 2 | 4 |

%e ----------------+---------------------------+-------+---+---+---

%e 6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 2 3 | ` | ` |

%e 9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 2 3 | ` | ` |

%e 3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 2 3 | ` | ` |

%e 2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 2 3 | ` | ` |

%e 4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 2 3 | ` | ` |

%e 1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 2 3 | ` | ` |

%e 2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 2 3 | ` | ` |

%e 1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 2 3 | 8 | ` |

%e ----------------+---------------------------+-------+---+---+---

%e 5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 2 4 | ` | ` |

%e 7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 2 4 | ` | ` |

%e 8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 2 4 | ` | ` |

%e 1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 2 4 | ` | ` |

%e 16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 2 4 | ` | ` |

%e 1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 2 4 | ` | ` |

%e 1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 2 4 | ` | ` |

%e 1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 2 4 | 8 |16 |20

%e ================================================================

%e a = this sequence

%e g = rote weight in gammas = A062537

%e q = primal code character = A108352

%e h = rote height in gammas = A109301

%e r = number in (g,q,h) set = A113200

%e s = count in (g, q) class = A112869

%e t = count in weight class = A061396

%Y Cf. A061396, A062504, A062537, A062860, A106177, A106178.

%Y Cf. A108352, A108353, A108370 to A108374, A109300, A109301.

%Y Cf. A111791 to A111801, A112868, A112869, A112870, A112871.

%Y Cf. A113197, A113198, A113200.

%K nonn,tabf

%O 1,2

%A _Jon Awbrey_, Oct 18 2005