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%I #23 Nov 11 2020 02:05:53
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum {n>=0} 1/3^(2^n).
%H Harry J. Smith, <a href="/A078885/b078885.txt">Table of n, a(n) for n = 0..20000</a>
%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 -Sum_{k>=1} mu(2*k)/(3^k - 1), where mu is the Möbius function (A008683). - _Amiram Eldar_, Jul 12 2020
%e 0.456942562477639661115491826166903037989942599713831192091056874309982...
%t RealDigits[ N[ Sum[1/3^(2^n), {n, 0, Infinity}], 110]] [[1]]
%o (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
%Y Cf. A004200 (continued fraction), A011764.
%Y Similar sums: A007404, A078585, A078886, A078887, A078888, A078889, A078890, A036987.
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, Dec 11 2002
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