%I A124091
%S A124091 2,4,1,0,2,7,8,7,9,7,2,0,7,8,6,5,8,9,1,7,9,4,0,4,3,0,2,4,4,7,1,0,6,3,1,
%T A124091 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 A124091 5,1,6,8,2,6,0,2,7,9,4,5,3,5,1,6,1,2,3,3,0,1,2,1,4,5,9,0,2,3,3,2,8,5,1
%N A124091 Decimal expansion of Fibonacci binary constant: Sum{i=0..inf} (1/2)^fibonacci(i).
%H A124091 Harry J. Smith, <a href="b124091.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A124091 D. H. Bailey, J. M. Borwein, R. E. Crandall and C. Pomerance, <a href="http:/
               /repositories.cdlib.org/lbnl/LBNL-53654/">On the binary expansions 
               of algebraic numbers</a>, LBNL-53854.
%F A124091 Sum_{i=0..infinity) 1/2^[A000045(i)].
%e A124091 2.4102787972078658917940430244710631444834239245952787725932..
%t A124091 RealDigits[ N[ Sum[(1/2)^Fibonacci[i], {i, 0, Infinity}], 111]][[1]] 
               - Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 26 2006
%o A124091 (PARI) { a=0 ; for(n=0,30, a += 1/(2^fibonacci(n)) ; print(a+0.0) ; ) 
               ; }
%o A124091 (PARI) { default(realprecision, 20080); x=suminf(k=0, 1/2^fibonacci(k)); 
               for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b124091.txt", n, 
               " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 
               04 2009]
%Y A124091 Equals A084119 + 1. Cf. A007404 (Kempner-Mahler number); continued fraction, 
               A125600.
%Y A124091 Cf. A006518, A084119. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 04 2009]
%Y A124091 Sequence in context: A115407 A010586 A070678 this_sequence A067849 A164268 
               A152433
%Y A124091 Adjacent sequences: A124088 A124089 A124090 this_sequence A124092 A124093 
               A124094
%K A124091 cons,nonn
%O A124091 1,1
%A A124091 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 25 2006
%E A124091 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 26 2006
%E A124091 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009