A006467 - OEIS

%I M3206 #26 Aug 30 2017 17:50:32

%S 0,4,3,1,3,5,1,3,5,3,3,1,5,3,1,3,3,5,3,1,3,5,1,3,3,5,3,1,5,3,1,3,5,3,

%T 3,1,3,5,1,3,5,3,3,1,5,3,1,3,5,3,3,1,3,5,1,3,3,5,3,1,5,3,1,3,3,5,3,1,

%U 3,5,1,3,5,3,3,1,5,3,1,3,3,5,3,1,3,5,1,3,3,5,3,1,5,3,1,3,3,5,3,1,3,5,1,3,5

%N Continued fraction for Sum_{n>=0} (-1)^n/3^(2^n).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harry J. Smith, <a href="/A006467/b006467.txt">Table of n, a(n) for n = 0..20000</a>

%H J. Shallit, <a href="/A006463/a006463.pdf">Letter to N. J. A. Sloane with attachment, Aug. 1979</a>

%H Jeffrey Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Papers/scf.ps">Simple continued fractions for some irrational numbers</a>. J. Number Theory 11 (1979), no. 2, 209-217 <a href="http://dx.doi.org/10.1016/0022-314X(79)90040-4">[DOI]</a>

%e 0.234415508674864614413415474... = 0 + 1/(4 + 1/(3 + 1/(1 + 1/(3 + ...)))). - _Harry J. Smith_, May 12 2009

%p u := 3: v := 7: Buv := [u,1,[0,u+1,u-1]]: for k from 2 to v do n := nops(Buv[3]): Buv := [u,Buv[2]+1,[seq(Buv[3][i],i=1..n-1),Buv[3][n]-(-1)^Buv[2],Buv[3][n]+(-1)^Buv[2],seq(Buv[3][n-i],i=1..n-2)]] od:seq(Buv[3][i],i=1..2^v); # first 2^v terms of A006467 # Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Dec 02 2002

%o (PARI) { allocatemem(932245000); default(realprecision, 20000); x=suminf(n=0, (-1)^n/3^(2^n)); x=contfrac(x); for (n=1, 20001, write("b006467.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 12 2009

%Y Cf. A160386 (decimal expansion). - _Harry J. Smith_, May 12 2009

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_

%E Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 19 2001