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 A014571 Consider the Morse-Thue sequence (A010060) as defining a binary constant and convert it to decimal. 15
 4, 1, 2, 4, 5, 4, 0, 3, 3, 6, 4, 0, 1, 0, 7, 5, 9, 7, 7, 8, 3, 3, 6, 1, 3, 6, 8, 2, 5, 8, 4, 5, 5, 2, 8, 3, 0, 8, 9, 4, 7, 8, 3, 7, 4, 4, 5, 5, 7, 6, 9, 5, 5, 7, 5, 7, 3, 3, 7, 9, 4, 1, 5, 3, 4, 8, 7, 9, 3, 5, 9, 2, 3, 6, 5, 7, 8, 2, 5, 8, 8, 9, 6, 3, 8, 0, 4, 5, 4, 0, 4, 8, 6, 2, 1, 2, 1, 3, 3, 3, 9, 6, 2, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse Constant, p. 437. LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Joerg Arndt, Matters Computational (The Fxtbook), p.726 ff Arturas Dubickas, On the distance from a rational power to the nearest integer, Journal of Number Theory, Volume 117, Issue 1, March 2006, Pages 222-239. Kurt Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Mathematische Annalen 101 (1929), pp. 342-366. R. Schroeppel and R. W. Gosper, HACKMEM #122 (1972). Eric Weisstein's World of Mathematics, Thue-Morse Constant FORMULA Equals Sum_{k>=0} A010060(n)*2^(-(k+1)). [Corrected by Jianing Song, Oct 27 2018] Equals Sum_{k>=1} 2^(-(A000069(k)+1)). - Jianing Song, Oct 27 2018 EXAMPLE 0.412454033640107597783361368258455283089... In hexadecimal, .6996966996696996... . MAPLE A014571 := proc()     local nlim, aold, a ;     nlim := ilog2(10^Digits) ;     aold := add( A010060(n)/2^n, n=0..nlim) ;     a := 0.0 ;     while abs(a-aold) > abs(a)/10^(Digits-3) do         aold := a;         nlim := nlim+200 ;         a := add( A010060(n)/2^n, n=0..nlim) ;     od:     evalf(%/2) ; end: A014571() ; # R. J. Mathar, Mar 03 2008 MATHEMATICA digits = 105; t[0] = 0; t[n_?EvenQ] := t[n] = t[n/2]; t[n_?OddQ] := t[n] = 1-t[(n-1)/2]; FromDigits[{t /@ Range[digits*Log[10]/Log[2] // Ceiling], -1}, 2] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 20 2014 *) 1/2-1/4*Product[1-2^(-2^k), {k, 0, Infinity}] // N[#, 105]& // RealDigits // First (* Jean-François Alcover, May 15 2014, after Steven Finch *) PROG (PARI) default(realprecision, 20080); x=0.0; m=67000; for (n=1, m-1, x=x+x; x=x+sum(k=0, length(binary(n))-1, bittest(n, k))%2); x=10*x/2^m; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b014571.txt", n, " ", d)); \\ Harry J. Smith, Apr 25 2009 (PARI) 1/2-prodinf(n=0, 1-1.>>2^n)/4 \\ Charles R Greathouse IV, Jul 31 2012 CROSSREFS Cf. A000069, A001969, A010060, A058631, A215016. Sequence in context: A021712 A307550 A309443 * A324466 A152523 A082903 Adjacent sequences:  A014568 A014569 A014570 * A014572 A014573 A014574 KEYWORD nonn,cons AUTHOR EXTENSIONS Corrected and extended by R. J. Mathar, Mar 03 2008 STATUS approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)