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%I #27 Aug 23 2021 00:46:49
%S 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,
%T 1,4,4,4,8,3,4,2,3,9,2,4,5,9,5,2,7,8,7,7,2,5,9,3,2,9,2,4,6,7,9,3,0,0,
%U 7,3,5,1,6,8,2,6,0,2,7,9,4,5,3,5,1,6,1,2,3,3,0,1,2,1,4,5,9,0,2,3,3,2,8,5,1
%N Decimal expansion of Fibonacci binary constant: Sum{i>=0} (1/2)^Fibonacci(i).
%C This constant is transcendental, see A084119. - _Charles R Greathouse IV_, Nov 12 2014
%H Harry J. Smith, <a href="/A124091/b124091.txt">Table of n, a(n) for n = 1..20000</a>
%H D. H. Bailey, J. M. Borwein, R. E. Crandall and C. Pomerance, <a href="https://escholarship.org/uc/item/44t5s388">On the binary expansions of algebraic numbers</a>, Journal de Théorie des Nombres de Bordeaux 16 (2004), 487-518.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals Sum_{i>=0} 1/2^A000045(i).
%F Equals A084119 + 1.
%e 2.4102787972078658917940430244710631444834239245952787725932...
%t RealDigits[ N[ Sum[(1/2)^Fibonacci[i], {i, 0, Infinity}], 111]][[1]] (* _Robert G. Wilson v_, Nov 26 2006 *)
%o (PARI) a=0 ; for(n=0,30, a += .5^fibonacci(n) ; print(a) ; )
%o (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)) \\ _Harry J. Smith_, May 04 2009
%Y Cf. A007404 (Kempner-Mahler number), A125600 (continued fraction), A084119 (essentially the same).
%Y Cf. A000301.
%K cons,nonn
%O 1,1
%A _R. J. Mathar_, Nov 25 2006
%E More terms from _Robert G. Wilson v_, Nov 26 2006
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