%I #24 Nov 12 2020 05:17:10
%S 3,1,6,4,2,1,5,0,9,0,2,1,8,9,3,1,4,3,7,0,8,0,7,9,7,3,7,5,3,0,5,2,5,2,
%T 2,1,7,0,3,3,1,1,3,7,5,9,2,0,5,5,2,8,0,4,3,4,1,2,1,0,9,0,3,8,4,3,0,5,
%U 5,6,1,4,1,9,4,5,5,5,3,0,0,0,6,0,4,8,5,3,1,3,2,4,8,3,9,7,2,6,5,6,1,7,5,5,8
%N Decimal expansion of Sum_{n>=0} 1/4^(2^n).
%H Harry J. Smith, <a href="/A078585/b078585.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)/(4^k - 1), where mu is the Möbius function (A008683). - _Amiram Eldar_, Jul 12 2020
%F Equals A007404 - 1/2. - _Kevin Ryde_, Nov 11 2020
%e 0.316421509021893143708079737530525221703311375920552804341210903843055...
%t RealDigits[ N[ Sum[1/4^(2^n), {n, 0, Infinity}], 110]][[1]]
%o (PARI) { default(realprecision, 20080); x=suminf(n=0, 1/4^(2^n)); x*=10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b078585.txt", n, " ", d)); } \\ _Harry J. Smith_, May 11 2009
%Y Continued fraction is given in A006464.
%Y Similar sums: A007404, A078885, A078886, A078887, A078888, A078889, A078890, A036987.
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, Dec 01 2002