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A054382 James Joyce's "Ulysses" sequence: number of digits in n^(n^n).

%I A054382 #53 Feb 16 2025 08:32:42
%S A054382 1,1,2,13,155,2185,36306,695975,15151336,369693100,10000000001,
%T A054382 297121486765,9622088391635,337385711567665,12735782555419983,
%U A054382 515003176870815368,22212093154093428530,1017876887958723919835,49390464231494436119285
%N A054382 James Joyce's "Ulysses" sequence: number of digits in n^(n^n).
%C A054382 Although Joyce mentions (9^9)^9, he clearly intended to refer to 9^(9^9).
%C A054382 (9^9)^9 is only 196627050475552913618075908526912116283103450944214766927315415537966391196809, whereas 9^(9^9) has 369693100 digits.
%D A054382 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.
%D A054382 David Wells: The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, 1986, p. 208.
%H A054382 Robert G. Wilson v, <a href="/A054382/b054382.txt">Table of n, a(n) for n = 0..1000</a> (first 57 terms from Carmine Suriano)
%H A054382 H. Havermann, <a href="http://chesswanks.com/seq/n^n^n/9^9^9/">9^9^9, in 33 volumes</a>.
%H A054382 J. Joyce, <a href="http://m.joyceproject.com/chapters/ithaca.html">Ulysses, Ithaca chapter</a>
%H A054382 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JoyceSequence.html">Joyce Sequence.</a>
%H A054382 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>
%F A054382 a(n) = floor(n^n*log_10(n)) + 1 for n > 0. - _Jianing Song_, Nov 21 2018
%e A054382 "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.
%e A054382 a(2)=2 since 2^(2^2)=2^4=16 has 2 digits. - _Carmine Suriano_, Feb 01 2011
%e A054382 a(0)=1 because 0^(0^0)=0^1=0, which has 1 digit. - _T. D. Noe_, Feb 01 2011
%p A054382 A055642 := proc(n) max(1,ilog10(n)+1) ; end proc:
%p A054382 A054382 := proc(n) A055642(n^(n^n)) ; end proc: # _R. J. Mathar_, Feb 01 2011
%t A054382 f[ j_ ] := 1 + Floor[ Log[10, j] j^j ]; Table[ f[j], {j, 2, 20} ]
%Y A054382 Cf. A002488, A055642, A066022.
%K A054382 nonn,base
%O A054382 0,3
%A A054382 Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 07 2000
%E A054382 More terms from _Michael Kleber_, May 07 2000