%I
%S 2,3,4,4,1,5,5,0,8,6,7,4,8,6,4,6,1,4,4,1,3,4,1,5,4,7,4,3,4,5,6,0,4,5,
%T 9,7,6,1,4,7,2,4,5,6,3,9,0,6,6,9,3,0,2,7,6,7,9,4,2,7,7,3,7,0,9,8,3,8,
%U 1,4,3,1,5,1,3,7,5,8,5,3,5,3,1,0,3,7,5,6,5,6,5,9,8,4,9,7,6,5,9,8,4,4,0,6,4
%N Decimal expansion of Sum_{n>=0}(1)^n/3^(2^n).
%C This sum is among forms which Kempner showed are transcendental.  _Kevin Ryde_, Sep 16 2019
%H Harry J. Smith, <a href="/A160386/b160386.txt">Table of n, a(n) for n = 0..20000</a>
%H Aubrey J. Kempner, <a href="https://www.jstor.org/stable/1988833">On Transcendental Numbers</a>, Transactions of the American Mathematical Society, Vol. 17, No. 4 (October 1916), pp. 476482.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 0.234415508674864614413415474345604597614724563906693027679427737098381...
%o (PARI) { default(realprecision, 20080); x=10*suminf(n=0, (1)^n/3^(2^n)); for (n=0, 20000, d=floor(x); x=(xd)*10; write("b160386.txt", n, " ", d)); }
%Y Cf. A006467 (continued fraction), A030300 (ternary expansion).
%K nonn,cons
%O 0,1
%A _Harry J. Smith_, May 12 2009
