Joyce Sequence, A054382
Antreas P. Hatzipolakis
xpolakis at otenet.gr
Tue May 9 20:25:23 CEST 2000
>Et al,
>
>In[3]:=Table[Ceiling[Log[10,j]*j^j],{j,1,20}]
>
>Out[3]=
>{0, 2, 13, 155, 2185, 36306, 695975, 15151336, 369693100, 10000000000,
^ ^^^^^^^^^^^^
----------------------------------------------------------------------------
Date: Sun, 7 May 2000 20:37:33 -0400 (EDT)
From: Michael Kleber <kleber at math.mit.edu>
To: kleber at math.mit.edu, xpolakis at otenet.gr
Subject: Re: Joyce Sequence
Cc: math-fun at optima.CS.Arizona.EDU
Oops -- #digits is 1+floor(log()), not ceiling(log()), so my 10000000000
ought to be 10000000001...
--mk
> Quoth 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 ??
> ...
> > 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.
>
> Happily, digital computers have come a long way since 1906.
>
> % math
> Mathematica 4.0 for Solaris
> Copyright 1988-1999 Wolfram Research, Inc.
> -- Motif graphics initialized --
>
> In[1]:= f[j_] := Ceiling[ Log[10,j] j^j ]
>
> In[2]:= Table[ f[j], {j,2,10} ]
>
> Out[2]= {2, 13, 155, 2185, 36306, 695975, 15151336, 369693100, 10000000000}
>
> --Michael Kleber
> kleber at math.mit.edu
----------------------------------------------------------------------------
>297121486765, 9622088391635, 337385711567665,
> 12735782555419983, 515003176870815368, 22212093154093428530,
>1017876887958723919835, 49390464231494436119285,
> 2529911258871481925207097, 136422882873335474575244148}
>
>But we know that the first entry should be 1 and not 0.
>
>Sequentially yours,
>Robert G. Wilson V
>rgwv at kspaint.com
APH
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