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%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