Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 21

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SeqFans,

Re: http://www.research.att.com/projects/OEIS?Anum=A007097
Cf: http://www.research.att.com/projects/OEIS?Anum=A109301

I've submitted the following comment on A007097, also known
as the "primeth recurrence", a(n+1) = prime(a(n)), a(0) = 1.

COMMENT FROM Jon Awbrey RE A007097

%I A007097
%S A007097 1,2,3,5,11,31,127,709
%C A007097 A007097(n) = Min {k : A109301(k) = n} = the first k whose rote height is n,
           the level set leader or minimum inverse function corresponding to A109301.
%Y A007097 Add A109301.
%O A007097 0
%K A007097 nonn,
%A A007097 Jon Awbrey, Jun 26 2005

At any rate, I think the comment is obvious from Bertrand's
Postulate and a contemplation of the following illustration:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 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 ` o-o ` o-o ` ` ` ` `
` ` ` | ` ` | ` ` | ` ` | ` ` | ` ` | ` ` ` ` ` `
O ` ` O ` ` O ` ` O ` ` O ` ` O ` ` O ` ` rote(k)
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
1 ` ` 2 ` ` 3 ` ` 5 ` ` 11` ` 31` ` 127 ` k ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
0 ` ` 1 ` ` 2 ` ` 3 ` ` 4 ` ` 5 ` ` 6 ` ` rhig(k)
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

But I thought I would check it out with the List.

Jon Awbrey

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