%I A143609
%S A143609 2,3,10,17,58,99,338,577,1970,3363,11482,19601,66922,114243,390050,
%T A143609 665857,2273378,3880899,13250218,22619537,77227930
%N A143609 Numerators of the upper principal and intermediate convergents to 2^(1/
               2).
%C A143609 The upper principal and intermediate convergents to 2^(1/2), beginning 
               with
%C A143609 2/1, 3/2, 10/7, 17/12, 58/41, form a strictly decreasing sequence;
%C A143609 essentially, numerators=A143609 and denominators=A084068.
%D A143609 Clark Kimberling, "Best lower and upper approximates to irrational numbers,
               " Elemente der Mathematik, 52 (1997) 122-126.
%D A143609 Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, 
               New York, 1966.
%H A143609 Creighton Kenneth Dement, <a href="a143608.txt">Comments on A143608 and 
               A143609</a>
%Y A143609 Sequence in context: A135061 A069156 A060744 this_sequence A066915 A070253 
               A147673
%Y A143609 Adjacent sequences: A143606 A143607 A143608 this_sequence A143610 A143611 
               A143612
%K A143609 nonn
%O A143609 1,1
%A A143609 Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008