Search: id:A079938
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%I A079938
%S A079938 1,2,3,8,99,33102,66317,265381,1360120
%N A079938 Greedy frac multiples of Pi: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=Pi.
%C A079938 The n-th greedy frac multiple of x is the smallest integer that does 
               not cause sum(k=1..n,frac(a(k)*x)) to exceed unity; an infinite number 
               of terms appear as the denominators of the convergents to the continued 
               fraction of x.
%e A079938 a(4) = 8 since frac(1x) + frac(2x) + frac(3x) + frac(8x) < 1, while frac(1x) 
               + frac(2x) + frac(3x) + frac(k*x) > 1 for all k>3 and k<8.
%p A079938 Digits := 100: a := []: s := 0: x := Pi: for n from 1 to 10000000 do: 
               temp := evalf(s+frac(n*x)): if (temp<1.0) then a := [op(a),n]: print(n): 
               s := s+evalf(frac(n*x)): fi: od: a;
%Y A079938 Cf. A002486 (denominators of convergents to Pi), A079934, A079937, A079939.
%Y A079938 Sequence in context: A003096 A042815 A005008 this_sequence A112237 A132502 
               A113840
%Y A079938 Adjacent sequences: A079935 A079936 A079937 this_sequence A079939 A079940 
               A079941
%K A079938 more,nonn
%O A079938 1,2
%A A079938 Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), 
               Jan 21 2003
%E A079938 One more term from Mark Hudson, Jan 30 2003

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