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 A007404 Decimal expansion of Sum_{n>=0} 1/2^(2^n). 18
 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 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Boris Adamczewski, The Many Faces of the Kempner Number, Journal of Integer Sequences, Vol. 16 (2013), #13.2.15. David H. Bailey, Jonathan M. Borwein, Richard E. Crandall, Carl Pomerance, On the Binary Expansions of Algebraic Numbers, Journal de ThÃ©orie des Nombres de Bordeaux, volume 16, number 3, 2004, pages 487-518.  Also LBNL-53854 2003, and authors' copies one, four. D. H. Bailey and H. R. P. Ferguson, Numerical results on relations between fundamental constants using a new algorithm, Mathematics of Computation, Vol.53 No. 188 (1989), 649-656. (Annotated scanned copy) F. R. Bernhart & N. J. A. Sloane, Emails, April-May 1994 Aubrey J. Kempner, On transcendental numbers, Transactions of the American Mathematical Society 17 (1916), pp. 476-482. Simon Plouffe, Plouffe's Inverter, sum(1/2^(2^n), n=0..infinity); to 20000 digits Simon Plouffe, sum(1/2^(2^n), n=0..infinity to 1024 digits Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217. 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 (PARI) suminf(k = 0, 1/(2^(2^k))) \\ Michel Marcus, Mar 26 2017 (PARI) suminf(k=0, 1.>>2^k) \\ Charles R Greathouse IV, Nov 07 2017 CROSSREFS Cf. A007400, A078885, A078585, A078886, A078887, A078888, A078889, A078890, A036987. Sequence in context: A176456 A033812 A019717 * A299627 A157697 A281785 Adjacent sequences:  A007401 A007402 A007403 * A007405 A007406 A007407 KEYWORD nonn,cons AUTHOR EXTENSIONS Edited by Robert G. Wilson v, Dec 11 2002 Deleted old PARI program Harry J. Smith, May 20 2009 STATUS approved

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Last modified October 25 16:00 EDT 2020. Contains 338012 sequences. (Running on oeis4.)