Joyce Sequence

[Antreas P. Hatzipolakis]

For a_n = n^n^n, let's define as "Joyce's sequence" the sequence:
j_n = the number of digits of a_n, that is:
1, 2, j_3, j_4, j_5, j_6, j_7, j_8, 369693100, j_10, .....

This sequernce is of some historical interest (see below).

Question: j_3,...,j_8  ??


Antreas

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From: xpolakis at otenet.gr (Antreas P. Hatzipolakis)
Subject: Re: [HM] Mathematics in Literature
To: historia-matematica at chasque.apc.org
Date: Sun, 7 May 2000 20:23:58 +0300 (EET DST)

Emmanuel Cardona wrote:

> I have found an interesting reference to the cycloid in Moby Dick Chapter 96:

Another great work with mathematical references is Joyce's _Ulysses_

Here is a quote:

"Because some years previously in 1886 when occupied with the problem of
the quadrature of the circle he had learned of the existence of a number
computed to a relative degree of accuracy to be of such magnitude and of
so many places, e.g., the 9th power of the 9th power of 9, that, the result
having been obtained, 33 closely printed volumes of 1000 pages each of
innumerable quires and reams of India paper would have to be requisitioned
in order to contain the complete tale of its printed integers of units, tens,
hundreds, thousands, tens of thousands, hundreds of thousands, millions,
tens of millions, hundreds of millions, billions, the nucleus of the nebula
of every digit of every series containing succinctly the potentiality of
being raised to the utmost kinetic elaboration of any power of any of its
powers".
James Joyce, _Ulysses_ (chapter: Ithaca)

On-line version at:

        http://www.edunet.ie/books/ulysses/ithaca.html

Comment:
C. A. Laisant (1906) proved that the number of digits of Joyce's number
(9^9^9) is 369,693,100.  H. S. Uhler (1947) published the log of the number
to 250 decimal places.
See: David Wells: the Penguin Dictionary of Curious and Interesting Numbers.
Penguin Books, 1986, p. 208

Antreas

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