|
|
A007404
|
|
Decimal expansion of Sum_{n>=0} 1/2^(2^n).
|
|
23
|
|
|
8, 1, 6, 4, 2, 1, 5, 0, 9, 0, 2, 1, 8, 9, 3, 1, 4, 3, 7, 0, 8, 0, 7, 9, 7, 3, 7, 5, 3, 0, 5, 2, 5, 2, 2, 1, 7, 0, 3, 3, 1, 1, 3, 7, 5, 9, 2, 0, 5, 5, 2, 8, 0, 4, 3, 4, 1, 2, 1, 0, 9, 0, 3, 8, 4, 3, 0, 5, 5, 6, 1, 4, 1, 9, 4, 5, 5, 5, 3, 0, 0, 0, 6, 0, 4, 8, 5, 3, 1, 3, 2, 4, 8, 3, 9, 7, 2, 6, 5, 6, 1, 7, 5, 5, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Kempner shows that numbers of a general form (which includes this constant) are transcendental. - Charles R Greathouse IV, Nov 07 2017
|
|
REFERENCES
|
M. J. Knight, An "oceans of zeros" proof that a certain non-Liouville number is transcendental, The American Mathematical Monthly, Vol. 98, No. 10 (1991), pp. 947-949.
|
|
LINKS
|
David H. Bailey, Jonathan M. Borwein, Richard E. Crandall, and Carl Pomerance, On the Binary Expansions of Algebraic Numbers, Journal de Théorie des Nombres de Bordeaux, volume 16, number 3, 2004, pages 487-518. Also LBNL-53854 2003, and authors' copies one, four.
|
|
FORMULA
|
Equals -Sum_{k>=1} mu(2*k)/(2^k - 1) = Sum_{k>=1, k odd} mu(k)/(2^k - 1). - Amiram Eldar, Jun 22 2020
|
|
EXAMPLE
|
0.81642150902189314370....
|
|
MATHEMATICA
|
RealDigits[ N[ Sum[1/2^(2^n), {n, 0, Infinity}], 110]] [[1]]
|
|
PROG
|
(PARI) default(realprecision, 20080); x=suminf(n=0, 1/2^(2^n)); x*=10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b007404.txt", n, " ", d)); \\ Harry J. Smith, May 07 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|