Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 12

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Re: A108374 [not ready for prime time]

Cf: http://www.research.att.com/projects/OEIS?Anum=A108352

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  =  2^2 3^3 7^1  =  1:2 2:3 4:1  =  4 -> 1 -> 2 -> 3

(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

Comment:

The following are a few numbers with a primal code characteristic of 4,
but they are not necessarily the only ones in the interval [1, 245000].
I think that 756 is the first number with a primal code char of 4, but
I'm not absolutely certain.

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

Jon Awbrey

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