Search: id:A012245
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%I A012245
%S A012245 1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%T A012245 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A012245 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A012245 Characteristic function of factorial numbers; also decimal expansion 
               of Liouville's number or Liouville's constant).
%C A012245 Read as decimal fraction 1100010... in any base > 1 (arbitrary decimal 
               point) Lioville's numbers are transcendental; read as a continued 
               fraction it is also transcendental [G. H. Hardy and E. M. Wright, 
               Th. 192].
%C A012245 a(A000142(n)) = 1; a(A063992(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 11 2008]
%D A012245 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 162.
%D A012245 T. W. Koerner, Fourier Analysis, Camb. Univ. Press 1988, p. 177.
%D A012245 J. Liouville, C. R. Acad. Sci. Paris 18, 883-885 and 993-995, 1844.
%D A012245 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               58.
%H A012245 Harry J. Smith, <a href="b012245.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A012245 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%H A012245 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A012245 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LiouvillesConstant.html">Link to a section of The World of Mathematics.</
               a>
%H A012245 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%F A012245 G.f.: sum(i=1, oo, x^product(j=1, i, j)) - Jon Perry (perry(AT)globalnet.co.uk), 
               Mar 31 2004
%e A012245 a(25) = a(26) =..= a(119) = 0 because 4! = 24 and 5! = 120
%e A012245 0.110001000000000000000001000000000000000000000000000000000000000000000... 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2009]
%o A012245 (PARI) { default(realprecision, 20080); x=10*suminf(n=1, 1.0/10^n!) + 
               1/10^20040; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b012245.txt", 
               n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 15 2009]
%Y A012245 Cf. A000142.
%Y A012245 Cf. A058304 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 15 2009]
%Y A012245 Sequence in context: A113052 A117964 A094875 this_sequence A089801 A089802 
               A143064
%Y A012245 Adjacent sequences: A012242 A012243 A012244 this_sequence A012246 A012247 
               A012248
%K A012245 nonn,nice
%O A012245 1,1
%A A012245 N. J. A. Sloane (njas(AT)research.att.com).

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