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 A160386 Decimal expansion of Sum_{n>=0}(-1)^n/3^(2^n). 4

%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. 476-482.

%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=(x-d)*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

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Last modified September 18 16:05 EDT 2020. Contains 337169 sequences. (Running on oeis4.)