Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 20

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Re: A109301 [pending]

%I A109301
%S A109301 0, 1, 2, 2, 3, 2, 3, 3, 2, 3, 4, 2, 3, 3, 3, 3, 4, 2, 4, 3
%N A109301 a(n) = rhig(n) = rote height in gamma's of n, where the "rotes"
           of positive integers are defined and illustrated in connection
           with A061396, and where "gamma" refers to a graph of the form:

           o--o
           |
           o

%e A109301 Example.  Writing (prime(i))^j as i:j, we have:

           802701 = 2:2 8638:1
           8638   = 1:1 4:1 113:1
           113    = 30:1
           30     = 1:1 2:1 3:1
           4      = 1:2
           3      = 2:1
           2      = 1:1
           1      = { }

           So rote(802701) is the graph:
           ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
           ` ` ` ` ` ` ` ` ` ` ` ` ` o-o
           ` ` ` ` ` ` ` ` ` ` ` ` ` | `
           ` ` ` ` ` ` ` ` ` ` ` o-o o-o
           ` ` ` ` ` ` ` ` ` ` ` | ` | `
           ` ` ` ` ` ` ` o-o o-o o-o o-o
           ` ` ` ` ` ` ` | ` | ` | ` | `
           ` ` ` ` ` ` o-o ` o===o===o-o
           ` ` ` ` ` ` | ` ` | ` ` ` ` `
           o-o o-o o-o o-o ` o---------o
           | ` | ` | ` | ` ` | ` ` ` ` `
           o---o ` o===o=====o---------o
           |`  ` ` | ` ` ` ` ` ` ` ` ` `
           O=======O ` ` ` ` ` ` ` ` ` `
           ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
           Here, "extended lines of identity" (eloi)
           indicate identified nodes, and capital O
           is the root node.

           So rhig(802701) = 6.

%Y A109301 A061396, A062504, A062537, A062860, A106177, A108352, A108371
%O A109301 1
%K A109301 nonn
%A A109301 Jon Awbrey, Jun 24 2005

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