Search: id:A006466
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%I A006466 M0049
%S A006466 1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,1,1,1,1,
%T A006466 1,1,2,1,1,1,1,2,1,2,1,1,1,1,1,1,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,1,1,1,2,
%U A006466 1,1,1,1,1,1,1,2,1,1,1,1,2,1,2,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,2
%N A006466 Continued fraction expansion of C = 2*sum( 1/2^(2^n), n=0 to infinity 
               ).
%C A006466 C arises when looking for a sequence b(n) such that : b(1)=0, b(n+1) 
               is the smallest integer > b(n) such that the continued fraction for 
               1/2^b(1)+1/2^b(2)+...+1/2^b(n+1) contains only 1's or 2's. Because 
               b(n)=2^n-1 and C = sum(k>=0,1/2^b(k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Nov 03 2002
%D A006466 J. O. Shallit, Simple continued fractions for some irrational numbers. 
               J. Number Theory 11 (1979), no. 2, 209-217.
%D A006466 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006466 Harry J. Smith, <a href="b006466.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A006466 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.
%F A006466 Recurrence: a(5n)=a(5n+1)=a(2)=a(5n+3)=a(20n+14)=a(40n+9)=1, a(20n+4)=a(40n+29)=2, 
               a(5n+2)=3-a(5n-1), a(20n+19)=a(10n+9). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               May 17 2005
%e A006466 1.632843018043786287416159475... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + ...)))) 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
%o A006466 (PARI) { allocatemem(932245000); default(realprecision, 10000); x=suminf(n=0, 
               1/2^(2^n)); x=contfrac(2*x); for (n=1, 20001, write("b006466.txt", 
               n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 09 2009]
%Y A006466 Cf. A076214 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 09 2009]
%Y A006466 Sequence in context: A072911 A053150 A163379 this_sequence A086597 A031214 
               A056059
%Y A006466 Adjacent sequences: A006463 A006464 A006465 this_sequence A006467 A006468 
               A006469
%K A006466 nonn,cofr
%O A006466 0,5
%A A006466 N. J. A. Sloane (njas(AT)research.att.com).
%E A006466 Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), 
               Jun 19 2001

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