A014572 Continued fraction for Thue-Morse constant.

0, 2, 2, 2, 1, 4, 3, 5, 2, 1, 4, 2, 1, 5, 44, 1, 4, 1, 2, 4, 1, 1, 1, 5, 14, 1, 50, 15, 5, 1, 1, 1, 4, 2, 1, 4, 1, 43, 1, 4, 1, 2, 1, 3, 16, 1, 2, 1, 2, 1, 50, 1, 2, 424, 1, 2, 5, 2, 1, 1, 1, 5, 5, 2, 22, 5, 1, 1, 1, 1274, 3, 5, 2, 1, 1, 1, 4, 1, 1, 15, 154, 7, 2, 1, 2, 2, 1, 2, 1, 1, 50

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• cofr

Examples

			A014571 = 0.4124540336401075977833613... = 0 + 1/(2 + 1/(2 + 1/(2 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 25 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• M. Beeler, R. W. Gosper, and R. Schroeppel, HAKMEM. Cambridge, MA: Mass. Institute of Technology Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972, Item 122, page 56. Also HTML transcription.
• Y. Bugeaud, On the rational approximation to the Thue-Morse-Mahler numbers, Ann. Inst. Fourier, Grenoble, 61 (2011), pp. 2065-2076. See p. 2068.
• Y. Bugeaud and M. Queffélec, On Rational Approximation of the Binary Thue-Morse-Mahler Number, Journal of Integer Sequences, 16 (2013), #13.2.3.
• Eric Weisstein's World of Mathematics, Thue-Morse Constant.
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A014571.

Programs

Mathematica

P = Sum[If[OddQ[Count[IntegerDigits[n, 2], 1]], 2^(-n-1), 0], {n, 0, 400}]; ContinuedFraction[P, 91] (* Jean-François Alcover, Oct 23 2012 *)
(* ThueMorse function needs $Version >= 10.2 *)
P = FromDigits[{ThueMorse /@ Range[0, 400], 0}, 2];
ContinuedFraction[P, 91] (* Jean-François Alcover, Jan 30 2020 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=0.0; m=70000; for (n=1, m-1, x=x+x; x=x+sum(k=0, length(binary(n))-1, bittest(n, k))%2); x=x/2^m; y=contfrac(x); for (n=1, 20001, write("b014572.txt", n-1, " ", y[n])); } \\ Harry J. Smith, Apr 25 2009