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%I
%S 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,
%T 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,
%U 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
%N Consider the Morse-Thue sequence (A010060) as defining a binary constant and convert it to decimal.
%C The constant is Sum A010060(n)*2^(-n).
%D Kurt Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Mathematische Annalen 101 (1929), pp. 342-366.
%H Harry J. Smith, <a href="/A014571/b014571.txt">Table of n, a(n) for n = 0..20000</a>
%H R. Schroeppel and R. W. Gosper, <a href="http://www.inwap.com/pdp10/hbaker/hakmem/series.html#item122">HACKMEM #122</a> (1972).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Thue-MorseConstant.html">Thue-Morse Constant</a>
%e 0.412454033640107597783361368258455283089...
%p A010060 := proc(n) add(i,i=convert(n,base,2)) mod 2 ; end: 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
%o (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)); } [From _Harry J. Smith_, Apr 25 2009]
%o (PARI) 1/2-prodinf(n=0,1-1.>>2^n)/4 \\ _Charles R Greathouse IV_, Jul 31 2012
%Y Cf. A010060, A058631, A215016.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_
%E Corrected and extended by _R. J. Mathar_, Mar 03 2008
%E Fixed my PARI program, had -n _Harry J. Smith_, May 19 2009
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