Riffs & Rotes & A061396 & A062504?

[Jon Awbrey]

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Re:

Notes on A062504 [pending]

Table 3.  Triangle in which k-th row lists natural number
          values for the collection of riffs with k nodes:
--o------------------------------------------------------------------------------
k | natural numbers n such that |riff(n)| = k
--o------------------------------------------------------------------------------
0 |    1;
1 |    2;
2 |    3,    4;
3 |    5,    6,    7,    8,     9,    16;
4 |   10,   11,   12,   13,    14,    17,     18,     19,     23,     25,
  |   27,   32,   49,   53,    64,    81,    128,    256,    512,  65536;
5 |   15,   20,   21,   22,    24,    26,     28,     29,     31,     34,
  |   36,   37,   38,   41,    43,    46,     48,     50,     54,     59,
  |   61,   67,   83,   97,    98,   103,    106,    121,    125,    131,
  |  162,  169,  227,  241,   243,   289,    311,    343,    361,    419,
  |  529,  625,  719,  729,  1024,  1619,   2048,   2187,   2401,   2809,
  | 3671, 4096, 6561, 8192, 16384, 19683, 131072, 262144, 524288, 821641,
  | 8388608,  33554432,  43046721,  134217728,  4294967296,  562949953421312,
  | 9007199254740992,  18446744073709551616,  2417851639229258349412352,
  | 2^128,  2^256,  2^512,  2^65536;
  |
--o------------------------------------------------------------------------------


30 = p^1 p^2 p^3 = p.p< .p<       
                       p   p<
                             p
=> |riff(30)| = 6

and 30 is the least number not in the above table,
so we have Min Seq = 1, 2, 3, 5, 10, 15, 30, ...
which is not in EIS.

Unless I have made the classic mistake of staying up too late again.

Which I will remedy, post haste.

Jon

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