Search: id:A084119
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%I A084119
%S A084119 1,4,1,0,2,7,8,7,9,7,2,0,7,8,6,5,8,9,1,7,9,4,0,4,3,0,2,4,4,7,1,0,6,3,1,
%T A084119 4,4,4,8,3,4,2,3,9,2,4,5,9,5,2,7,8,7,7,2,5,9,3,2,9,2,4,6,7,9,3,0,0,7,3,
%U A084119 5,1,6,8,2,6,0,2,7,9,4,5,3,5,1,6,1,2,3,3
%N A084119 Decimal expansion of the Fibonacci binary number, sum(k>0, 1/2^F(k)), 
               where F(k)=A000045(k).
%C A084119 The Fibonacci binary number 1.41027879720... is known to be transcendental.
%D A084119 J. H. Loxton and A. van der Poorten, Bull. AMS 16 (1977), 15-47.
%D A084119 J. Shallit and A. van der Poorten, Can. J. Math. 45 (1993), 1067-79.
%H A084119 Harry J. Smith, <a href="b084119.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A084119 D. Bailey et al., <a href="http://crd.lbl.gov/~dhbailey/dhbpapers/algebraic.pdf">
               On the binary expansions of algebraic numbers</a>
%o A084119 (PARI) suminf(k=1,1/2^fibonacci(k))
%o A084119 (PARI) { default(realprecision, 20080); x=suminf(k=1, 1/2^fibonacci(k)); 
               for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b084119.txt", n, 
               " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 
               04 2009]
%Y A084119 Cf. A010056, A079586. See A124091 for another version.
%Y A084119 Cf. A006518, A124091. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 04 2009]
%Y A084119 Sequence in context: A124539 A096501 A062862 this_sequence A166073 A122899 
               A021713
%Y A084119 Adjacent sequences: A084116 A084117 A084118 this_sequence A084120 A084121 
               A084122
%K A084119 nonn,cons
%O A084119 1,2
%A A084119 Ralf Stephan (ralf(AT)ark.in-berlin.de), May 18 2003
%E A084119 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009

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