Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 17

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Re: A108374 [pending]

%I A108374
%S A108374 756, 1176, 1188, 1200
%N A108374 Numbers whose primal code characteristic = 4,
           that is, positive n for which A108352(n) = 4.
%Y A108374 Cf. A108352, A108370, A108371, A108372, A108373.
%O A108374 1
%K A108374 nonn
%A A108374 Jon Awbrey (jawbrey at att.net), Jun 16 2005

Example:

The primal code characteristic of 756 is 4, that is, A108352(756) = 4,
because 756 has this sequence of powers under primal code composition:

   (756 o)^2 = (1:2 2:3 4:1) o (1:2 2:3 4:1) = (1:3 4:2) = 392
   (756 o)^3 =     (1:3 4:2) o (1:2 2:3 4:1) =     (4:3) = 343
   (756 o)^4 =         (4:3) o (1:2 2:3 4:1) = 1

The primal function digraph of 756 is 4 -> 1 -> 2 -> 3.

Comment:

The following numbers have primal function digraphs of the shape
a -> b -> c -> d, where the 4-tuple <a, b, c, d> ranges over the
24 permutations of {1, 2, 3, 4}:

     756,  1176,  1200,   1400,   1620,   2160,   3920,   4536,
    6615,  6860, 14175,  15000,  16200,  16464,  17500,  21168,
   25725, 67500, 91875, 111132, 118125, 137200, 138915, 245000.

However, these are not the only numbers of characteristic 4
in the interval [1, 245000], as we can see from the example
of 1188, with the primal function digraph 5 -> 1 -> 2 -> 3.

Cf.  A108352.  http://www.research.att.com/projects/OEIS?Anum=A108352
Cf.  R&R 15.   http://stderr.org/pipermail/inquiry/2005-June/002799.html

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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