%I A007400
%S A007400 0,1,4,2,4,4,6,4,2,4,6,2,4,6,4,4,2,4,6,2,4,4,6,4,2,6,4,2,4,6,4,4,2,
%T A007400 4,6,2,4,4,6,4,2,4,6,2,4,6,4,4,2,6,4,2,4,4,6,4,2,6,4,2,4,6,4,4,2,4,
%U A007400 6,2,4,4,6,4,2,4,6,2,4,6,4,4,2,4,6,2,4,4,6,4,2,6,4,2,4,6,4,4,2,6,4
%N A007400 Continued fraction for Sum[ 1/2^(2^n),{n,0,Infinity} ] = 0.8164215090218931...
%D A007400 Shallit, Jeffrey; Simple continued fractions for some irrational numbers. 
               J. Number Theory 11 (1979), no. 2, 209-217.
%H A007400 Harry J. Smith, <a href="b007400.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A007400 H. Cohn, <a href="http://arXiv.org/abs/math.NT/0008221">Symmetry and 
               specializability in continued fractions</a>
%H A007400 J. O. 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.
%H A007400 A. J. van der Poorten, <a href="http://www-centre.mpce.mq.edu.au/alfpapers/
               a075.pdf">An introduction to continued fractions</a>
%H A007400 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A007400 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%F A007400 Recurrence: a(0)=0, a(1)=1, a(2)=4, a(8n)=a(8n+3)=2, a(8n+4)=a(8n+7)=a(16n+5)=a(16n+14)=4, 
               a(16n+6)=a(16n+13)=6, a(8n+1)=a(4n+1), a(8n+2)=a(4n+2). - Ralf Stephan 
               (ralf(AT)ark.in-berlin.de), May 17 2005
%e A007400 0.816421509021893143708079737... = 0 + 1/(1 + 1/(4 + 1/(2 + 1/(4 + ...)))) 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 01 2009]
%o A007400 (PARI) a(n)=if(n<3,[0,1,4][n+1],if(n%8==1,a((n+1)/2),if(n%8==2,a((n+2)/
               2),[2,0,0,2,4,4,6,4,2,0,0,2,4,6,4,4][(n%16)+1]))) /* from R. Stephan 
               */
%o A007400 (PARI) a(n)=contfrac(suminf(n=0,1/2^(2^n)))[n+1]
%o A007400 (PARI) { allocatemem(932245000); default(realprecision, 26000); x=suminf(n=0, 
               1/2^(2^n)); x=contfrac(x); for (n=1, 20001, write("b007400.txt", 
               n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 07 2009]
%Y A007400 Cf. A007404.
%Y A007400 Cf. A089267.
%Y A007400 Sequence in context: A095382 A135282 A103859 this_sequence A019921 A061469 
               A021706
%Y A007400 Adjacent sequences: A007397 A007398 A007399 this_sequence A007401 A007402 
               A007403
%K A007400 nonn,cofr
%O A007400 0,3
%A A007400 Simon Plouffe (simon.plouffe(AT)gmail.com), Jeff Shallit (shallit(AT)graceland.uwaterloo.ca)
%E A007400 Deleted old PARI program Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 20 2009