A078890 Decimal expansion of Sum {n>=0} 1/9^(2^n).

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

Offset: 0

Author

Robert G. Wilson v, Dec 11 2002

Keywords

• cons
• nonn

Examples

			0.123609229144306327782...
		

Links

• Aubrey J. Kempner, On Transcendental Numbers, Transactions of the American Mathematical Society, volume 17, number 4, October 1916, pages 476-482.
• Index entries for transcendental numbers

Crossrefs

Similar sums: A007404, A078885, A078585, A078886, A078887, A078888, A078889, A036987.

Programs

Mathematica

RealDigits[ N[ Sum[1/9^(2^n), {n, 0, Infinity}], 110]][[1]]

PARI

suminf(n=0, 1/9^(2^n)) \\ Michel Marcus, Nov 11 2020

Formula

Equals A078885 - 1/3 = A078885 - A010701. - R. J. Mathar, Apr 23 2009

Equals -Sum_{k>=1} mu(2*k)/(9^k - 1), where mu is the Möbius function (A008683). - Amiram Eldar, Jul 12 2020