A078885 Decimal expansion of Sum {n>=0} 1/3^(2^n).

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

Offset: 0

Author

Robert G. Wilson v, Dec 11 2002

Keywords

• cons
• nonn

Examples

			0.456942562477639661115491826166903037989942599713831192091056874309982...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• 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

Cf. A004200 (continued fraction), A011764.

Similar sums: A007404, A078585, A078886, A078887, A078888, A078889, A078890, A036987.

Programs

Mathematica

RealDigits[ N[ Sum[1/3^(2^n), {n, 0, Infinity}], 110]] [[1]]

PARI

default(realprecision, 20080); x=suminf(n=0, 1/3^(2^n)); x*=10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b078885.txt", n, " ", d)); \\ Harry J. Smith, May 10 2009

Formula

Equals -Sum_{k>=1} mu(2*k)/(3^k - 1), where mu is the Möbius function (A008683). - Amiram Eldar, Jul 12 2020