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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: A236269 A010126 A021712 * A324466 A152523 A082903

Adjacent sequences:  A014568 A014569 A014570 * A014572 A014573 A014574

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein

EXTENSIONS

Corrected and extended by R. J. Mathar, Mar 03 2008

STATUS

approved

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Last modified March 24 19:48 EDT 2019. Contains 321448 sequences. (Running on oeis4.)