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A054382 James Joyce's "Ulysses" sequence: number of digits in n^(n^n). 2
1, 1, 2, 13, 155, 2185, 36306, 695975, 15151336, 369693100, 10000000001, 297121486765, 9622088391635, 337385711567665, 12735782555419983, 515003176870815368, 22212093154093428530, 1017876887958723919835, 49390464231494436119285 (list; graph; refs; listen; history; internal format)
OFFSET

0,3

COMMENTS

Although Joyce mentions (9^9)^9, he clearly intended to refer to 9^(9^9).

(9^9)^9 is only 196627050475552913618075908526912116283103450944214766927315415537966391196809, whereas 9^(9^9) has 369693100 digits.

REFERENCES

C. A. Laisant (1906) proved that the number of digits of a(9), 9^9^9, is 369693100. H. S. Uhler (1947) published the log of the number to 250 decimal places.

David Wells: The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, 1986, p. 208.

LINKS

J. Joyce, Ulysses, Ithaca chapter

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

H. Havermann, 9^9^9, in 33 volumes.

Carmine Suriano, Table of n, a(n) for n = 0..56

EXAMPLE

"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 17.

a(2)=2 since 2^(2^2)=2^4=16 has 2 digits. - Carmine Suriano, Feb 01 2011

a(0)=1 because 0^(0^0)=0^1=0, which has 1 digit. - T. D. Noe, Feb 01 2011

MAPLE

A055642 := proc(n) max(1, ilog10(n)+1) ; end proc:

A054382 := proc(n) A055642(n^(n^n)) ; end proc: # R. J. Mathar, Feb 01 2011

MATHEMATICA

f[ j_ ] := 1 + Floor[ Log[10, j] j^j ]; Table[ f[j], {j, 2, 20} ]

CROSSREFS

Sequence in context: A204554 A069736 A058192 * A062593 A192563 A014507

Adjacent sequences:  A054379 A054380 A054381 * A054383 A054384 A054385

KEYWORD

nonn,base

AUTHOR

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 07 2000

EXTENSIONS

More terms from Michael Kleber (michael.kleber(AT)gmail.com), May 07 2000.

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Last modified February 15 19:15 EST 2012. Contains 205852 sequences.