%I #14 Nov 12 2020 05:17:44

%S 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,

%T 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,

%U 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

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

%H Aubrey J. Kempner, <a href="https://doi.org/10.1090/S0002-9947-1916-1501054-4">On Transcendental Numbers</a>, Transactions of the American Mathematical Society, volume 17, number 4, October 1916, pages 476-482.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A078885 - 1/3 = A078885 - A010701. - _R. J. Mathar_, Apr 23 2009

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

%e 0.123609229144306327782...

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

%o (PARI) suminf(n=0, 1/9^(2^n)) \\ _Michel Marcus_, Nov 11 2020

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

%K cons,nonn

%O 0,2

%A _Robert G. Wilson v_, Dec 11 2002