[seqfan] Re: Experimental Number Theory, Part I : Tower Arithmetic
Georgi Guninski
guninski at guninski.com
Wed Jan 19 17:39:22 CET 2011
On Tue, Jan 18, 2011 at 08:37:35AM -0800, Jonathan Post wrote:
> Through a(48) the below seq seems to agree with A165412 Divisors of 2520.
>
> What's the reason, and is the arXiv paper and its Mathematica cited a
> basis for submitting the seq from page 3:
> g(x) = 1 + x + x^x + x^x^x + x^x^x^x + · · ·
>
> {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35,
> 36, 40, 42, 45, 56, 60, 63, 64, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180,
> 192, 210, 252, 280, 315, 320, 360, 420, 448, 504, 576, 630, 840
> , 960, 1260, 1344, 2240, 2520, 2880, 4032, 6720, 20160}
>
> Page 9 of the following is the source for the above values
>
> arXiv:1101.3026 [pdf, ps, other]
> Title: Experimental Number Theory, Part I : Tower Arithmetic
> Authors: Edinah K. Gnang
> Subjects: Number Theory (math.NT); Combinatorics (math.CO)
>
> We introduce in this section an Algebraic and Combinatorial
> approach to the theory of Numbers. The approach rests on the
> observation that numbers can be identified with familiar combinatorial
> objects namely rooted trees, which we shall here refer to as towers.
> The bijection between numbers and towers provides some insights into
> unexpected connexions between Number theory, combinatorics and
> discrete probability theory.
>
Aren't towers of exponents computationally intractable - Fermat
numbers already grow quite fast?
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