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%I #17 Oct 01 2014 15:25:14
%S 1,7,3,7,6,5,7,4,9,4,7,7,6,5,5,3,6,2,1,2,6,0,0,6,7,8,8,8,5,1,7,4,6,2,
%T 0,9,9,7,9,4,3,8,5,6,2,4,1,0,6,5,3,8,3,2,9,6,2,6,0,3,6,7,4,2,8,7,2,9,
%U 8,9,7,6,6,5,3,5,8,6,7,3,9,2,5,1,4,6,2,8,7,4,5,9,6,2,0,0,2,5,6,8,3,9,6
%N Decimal expansion of the value of a nonregular continued fraction giving tau/(3*tau-1), where tau is the Prouhet-Thue-Morse constant.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse Constant, p. 437.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Thue-MorseConstant.html">Thue-Morse Constant</a>
%F 2 - 1/(4 - 3/(16 - 15/(256 - 255/65536 - ...))).
%F Pattern is generated by 2^(2^n) and 2^(2^n)-1.
%e 1.737657494776553621260067888517462099794385624106538329626...
%p evalf(1/(3-1/(1/2-(1/4)*(product(1-1/2^(2^k), k=0..11)))), 120); # _Vaclav Kotesovec_, Oct 01 2014
%t (* 10 terms suffice to get 103 correct digits *) t = Fold[Function[2^2^#2 - (2^2^#2 - 1)/#1], 2, Reverse[Range[0, 10]]]; RealDigits[t, 10, 103] // First
%Y Cf. A010060, A014571, A058631.
%K nonn,cons
%O 1,2
%A _Jean-François Alcover_, Oct 01 2014