A343786 Decimal expansion of Sum_{k>=0} 2^(3^k)/(2^(2*(3^k)) + 2^(3^k) + 1).

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

Offset: 0

Author

Amiram Eldar, Apr 29 2021

Keywords

• nonn
• cons
• easy

Comments

Proven to be a transcendental number by Borwein and Coons (2008).

Examples

			0.39725264457801453528444061025296764648419265353335...
		

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.
• Index entries for transcendental numbers.

Crossrefs

Cf. A023365, A343785.

Programs

Mathematica

f[x_] := x/(x^2 + x + 1); RealDigits[Sum[f[2^(3^n)], {n, 0, 10}], 10, 100][[1]]

Formula

Equals Sum_{k>=1} A343785(k)/2^k.