%I A074065
%S A074065 0,1,1,2,3,3,4,5,5,6,6,7,8,8,9,10,10,11,12,12,13,13,14,15,15,16,17,17,
%T A074065 18,19,19,20,20,21,22,22,23,24,24,25,25,26,27,27,28,29,29,30,31,31,32,
%U A074065 32,33,34,34,35,36,36,37,38,38,39,39,40,41,41,42,43,43,44,45,45,46,46
%N A074065 Numerators a(n) of fractions slowly converging to sqrt(3): let a(1) = 
               0, b(n) = n - a(n); if (a(n) + 1) / b(n) < sqrt(3), then a(n+1) = 
               a(n) + 1, else a(n+1)= a(n).
%C A074065 a(n) + b(n) = n and as n -> +infinity, a(n) / b(n) converges to sqrt(3). 
               For all n, a(n) / b(n) < sqrt(3).
%F A074065 a(1) = 0. b(n) = n - a(n). If (a(n) + 1) / b(n) < sqrt(3), then a(n+1) 
               = a(n) + 1, else a(n+1) = a(n).
%F A074065 a(n) = floor(n*(3-sqrt(3))/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 04 2003
%e A074065 a(6)= 3 so b(6) = 6 - 3 = 3. a(7) = 4 because (a(6) + 1) / b(6) = 4/3 
               which is < sqrt(3). So b(7) = 7 - 4 = 3. a(8) = 5 because (a(7) + 
               1) / b(7) = 5/3 which is < sqrt(3).
%Y A074065 Cf. A074840.
%Y A074065 Sequence in context: A057361 A136409 A039729 this_sequence A024811 A131138 
               A093878
%Y A074065 Adjacent sequences: A074062 A074063 A074064 this_sequence A074066 A074067 
               A074068
%K A074065 easy,frac,nonn
%O A074065 0,4
%A A074065 Robert A. Stump (bee_ess107(AT)msn.com), Sep 15 2002