A343784 Decimal expansion of Sum_{k>=1} A065043(k)/2^k.

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

Author

Amiram Eldar, Apr 29 2021

Keywords

• nonn
• cons
• easy

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).

Examples

			0.58116231881196489297989866791811204585002418961440...
		

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.

Crossrefs

Cf. A008836, A028260, A065043.

Programs

Mathematica

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

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).