%I A074840
%S A074840 0,1,1,2,2,3,4,4,5,5,6,7,7,8,8,9,9,10,11,11,12,12,13,14,14,15,15,16,16,
%T A074840 17,18,18,19,19,20,21,21,22,22,23,24,24,25,25,26,26,27,28,28,29,29,30,
%U A074840 31,31,32,32,33,33,34,35,35,36,36,37,38,38,39,39,40,41,41,42,42,43,43
%N A074840 Numerators a(n) of fractions slowly converging to sqrt(2): let a(1) = 
               0, b(n) = n - a(n); if (a(n) + 1) / b(n) < sqrt(2), then a(n+1) = 
               a(n) + 1, else a(n+1)= a(n).
%C A074840 a(n) + b(n) = n and as n -> +infinity, a(n) / b(n) converges to sqrt(2). 
               For all n, a(n) / b(n) < sqrt(2).
%F A074840 a(1) = 0. b(n) = n - a(n). If (a(n) + 1) / b(n) < sqrt(2), then a(n+1) 
               = a(n) + 1, else a(n+1) = a(n).
%F A074840 a(n) = floor(n*(2-sqrt(2))). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 04 2003
%e A074840 a(6)= 3 so b(6) = 6 - 3 = 3. a(7) = 4 because (a(6) + 1) / b(6) = 4/3 
               which is < sqrt(2). So b(7) = 7 - 4 = 3. a(8) = 4 because (a(7) + 
               1) / b(7) = 5/3 which is not < sqrt(2).
%Y A074840 Cf. A001601.
%Y A074840 Sequence in context: A139327 A076905 A098295 this_sequence A064542 A076935 
               A019446
%Y A074840 Adjacent sequences: A074837 A074838 A074839 this_sequence A074841 A074842 
               A074843
%K A074840 easy,frac,nonn
%O A074840 1,4
%A A074840 Robert A. Stump (bee_ess107(AT)msn.com), Sep 09 2002