This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321071 #21 Feb 16 2025 08:33:57
%S A321071 8,2,4,9,0,8,0,6,7,2,8,0,2,1,5,1,9,5,5,6,6,7,2,2,7,3,6,5,1,6,9,1,0,5,
%T A321071 6,6,1,7,8,9,5,6,7,4,8,9,1,1,5,3,9,1,1,5,1,4,6,7,5,8,8,3,0,6,9,7,5,8,
%U A321071 7,1,8,4,7,3,1,5,6,5,1,7,7,9,2,7,6,0,9,0,8,0
%N A321071 Twice the Thue-Morse constant (A014571).
%C A321071 This is the value of the g.f. of A010060 at x = 1/2. This number is transcendental.
%D A321071 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.8, p. 437.
%H A321071 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Thue-MorseConstant.html">Thue-Morse Constant</a>.
%H A321071 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A321071 Equals Sum_{k>=0} A010060(k)*2^(-k) = 1 - (Product_{k>=0} (1 - 2^(-2^k)))/2.
%F A321071 Equals Sum_{k>=1} 2^(-A000069(k)).
%e A321071 Equals 2^(-1) + 2^(-2) + 2^(-4) + 2^(-7) + ... = 0.11010011001011010..._2 = 0.82490806728021519...
%t A321071 P = FromDigits[{ThueMorse /@ Range[0, 400], 0}, 2];
%t A321071 RealDigits[2P, 10, 105][[1]] (* _Jean-François Alcover_, Apr 21 2021 *)
%o A321071 (PARI) 1-prodinf(n=0, 1-1.>>2^n)/2
%Y A321071 Cf. A000069, A001969, A010060, A014571.
%K A321071 nonn,cons
%O A321071 0,1
%A A321071 _Jianing Song_, Oct 27 2018