Search: id:A143608
Results 1-1 of 1 results found.

%I A143608
%S A143608 1,4,7,24,41,140,239,816,1393,4756,8119,27720,47321,161564,275807,
%T A143608 941664,1607521,5488420,9369319,31988856,54608393
%N A143608 Numerators of the lower principal and intermediate convergents to 2^(1/
               2).
%C A143608 The lower principal and intermediate convergents to 2^(1/2), beginning 
               with
%C A143608 1/1, 4/3, 7/5, 24/17, 41/29, form a strictly increasing sequence;
%C A143608 essentially, numerators=A143608 and denominators=A079496.
%D A143608 Clark Kimberling, "Best lower and upper approximates to irrational numbers,
               " Elemente der Mathematik, 52 (1997) 122-126.
%D A143608 Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, 
               New York, 1966.
%H A143608 Creighton Kenneth Dement, <a href="a143608.txt">Comments on A143608 and 
               A143609</a>
%H A143608 C. Kimberling, <a href="http://dx.doi.org/10.1007/s000170050020">Best 
               lower and upper approximations to irrational numbers</a>, Elem. Math. 
               vol. 52 iss. 3 (1997) 122-126. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 08 2009]
%F A143608 Conjectures: a(n)=6*a(n-2)-a(n-4). G.f.: x*(1+4*x+x^2)/((x^2-2*x-1)*(x^2+2*x-1)). 
               a(2n)=A005319(n). a(2n+1)=A002314(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 17 2009]
%Y A143608 Sequence in context: A086968 A101824 A027946 this_sequence A079441 A129418 
               A073218
%Y A143608 Adjacent sequences: A143605 A143606 A143607 this_sequence A143609 A143610 
               A143611
%K A143608 nonn
%O A143608 1,2
%A A143608 Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008

Search completed in 0.001 seconds