%I A159243
%S A159243 2,4,8,15,24,41,85,159,314,651,1267,2496,4977,9889,19731,38945,77356,
%T A159243 154693,308051,615768,1229080
%N A159243 Number of elements in the continued fraction for sum(k=0,n,1/1+2^2^k)
%C A159243 Number of terms in the n-th partial sum of the Fermat Numbers Reciprocals.
%H A159243 Daniel Duverney, <a href="http://journal.ms.u-tokyo.ac.jp/pdf/jms080206.pdf">
               Irrationality of Fast Converging Series of Rational Numbers</a>, 
               Discrete Math., 294 (2005), 259-274. , <a href="http://arXiv.org/
               abs/math.CO/0312418">On non-squashing partitions</a>, Discrete Math., 
               294 (2005), 259-274.
%e A159243 The Reciprocals Fermat Numbers partial sum for k=3 (four terms), is: 
               1/3+1/5+1/17+1/257=39062/65535 expresed in continued fraction gives: 
               {0,1,1,2,9,1,2,1,1,2,2,1,2,1,5} that has 15 elements so: f(3)=15
%t A159243 Table[Length[ContinuedFraction[Sum[1/(1 + 2^2^k), {k, 0, v}]]], {v, 0, 
               20}]
%Y A159243 A056469
%Y A159243 Sequence in context: A094398 A026474 A082562 this_sequence A089140 A000125 
               A129961
%Y A159243 A051158 [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Nov 17 2009]
%Y A159243 Adjacent sequences: A159240 A159241 A159242 this_sequence A159244 A159245 
               A159246
%K A159243 nonn
%O A159243 1,1
%A A159243 Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Apr 06 2009