A124091 Decimal expansion of Fibonacci binary constant: Sum{i>=0} (1/2)^Fibonacci(i).

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, 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, 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

Offset: 1

Author

R. J. Mathar, Nov 25 2006

Keywords

• cons
• nonn

Comments

This constant is transcendental, see A084119. - Charles R Greathouse IV, Nov 12 2014

Examples

			2.4102787972078658917940430244710631444834239245952787725932...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• D. H. Bailey, J. M. Borwein, R. E. Crandall and C. Pomerance, On the binary expansions of algebraic numbers, Journal de Théorie des Nombres de Bordeaux 16 (2004), 487-518.
• Index entries for transcendental numbers

Crossrefs

Cf. A007404 (Kempner-Mahler number), A125600 (continued fraction), A084119 (essentially the same).

Cf. A000301.

Programs

Mathematica

RealDigits[ N[ Sum[(1/2)^Fibonacci[i], {i, 0, Infinity}], 111]][[1]] (* Robert G. Wilson v, Nov 26 2006 *)

PARI

a=0 ; for(n=0,30, a += .5^fibonacci(n) ; print(a) ; )

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

Formula

Equals Sum_{i>=0} 1/2^A000045(i).

Equals A084119 + 1.

Extensions

More terms from Robert G. Wilson v, Nov 26 2006