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A343784
Decimal expansion of Sum_{k>=1} A065043(k)/2^k.
1
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, 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, 2, 6, 6, 2, 3, 8, 4, 5, 0, 9, 7, 6, 2, 3, 9, 8, 6, 0, 1
OFFSET
0,1
COMMENTS
Named "the Liouville number" and conjectured to be a transcendental number by Borwein and Coons (2008).
The binary expansion of this constant is A065043 (with an offset 0).
LINKS
Peter Borwein and Michael Coons, Transcendence of the Gaussian Liouville number and relatives, arXiv:0806.1694 [math.NT], 2008.
Michael J. Coons, Some aspects of analytic number theory: parity, transcendence, and multiplicative functions, Ph.D. Thesis, Department of Mathematics, Simon Fraser University, 2009.
FORMULA
Equals Sum_{k>=1} (1+lambda(k))/2^(k+1), where lambda(k) = A008836(k) is Liouville's function.
Equals Sum_{k>=1} 1/2^A028260(k).
EXAMPLE
0.58116231881196489297989866791811204585002418961440...
MATHEMATICA
RealDigits[Sum[(LiouvilleLambda[n] + 1)/2^(n + 1), {n, 1, 400}], 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Amiram Eldar, Apr 29 2021
STATUS
approved