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Decimal expansion of Sum_{k>=1} A065043(k)/2^k.
1

%I #19 Jan 14 2024 12:55:57

%S 5,8,1,1,6,2,3,1,8,8,1,1,9,6,4,8,9,2,9,7,9,8,9,8,6,6,7,9,1,8,1,1,2,0,

%T 4,5,8,5,0,0,2,4,1,8,9,6,1,4,4,0,7,9,7,4,5,9,6,7,2,1,4,6,9,4,8,5,3,9,

%U 2,6,6,2,3,8,4,5,0,9,7,6,2,3,9,8,6,0,1

%N Decimal expansion of Sum_{k>=1} A065043(k)/2^k.

%C Named "the Liouville number" and conjectured to be a transcendental number by Borwein and Coons (2008).

%C The binary expansion of this constant is A065043 (with an offset 0).

%H Peter Borwein and Michael Coons, <a href="https://arxiv.org/abs/0806.1694">Transcendence of the Gaussian Liouville number and relatives</a>, arXiv:0806.1694 [math.NT], 2008.

%H Michael J. Coons, <a href="https://summit.sfu.ca/item/9417">Some aspects of analytic number theory: parity, transcendence, and multiplicative functions</a>, Ph.D. Thesis, Department of Mathematics, Simon Fraser University, 2009.

%F Equals Sum_{k>=1} (1+lambda(k))/2^(k+1), where lambda(k) = A008836(k) is Liouville's function.

%F Equals Sum_{k>=1} 1/2^A028260(k).

%e 0.58116231881196489297989866791811204585002418961440...

%t RealDigits[Sum[(LiouvilleLambda[n] + 1)/2^(n + 1), {n, 1, 400}], 10, 100][[1]]

%Y Cf. A008836, A028260, A065043.

%K nonn,cons,easy

%O 0,1

%A _Amiram Eldar_, Apr 29 2021