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%I #8 Mar 30 2012 18:39:15
%S 1,3,7,14,39,78,394,1001,2002,3003,9545,10546,27634,154257,398959,
%T 797918
%N Greedy frac multiples of e: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=e.
%C 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 a(4) = 14 since frac(1x) + frac(3x) + frac(7x) + frac(14x) < 1, while frac(1x) + frac(3x) + frac(7x) + frac(k*x) > 1 for all k>7 and k<14.
%p Digits := 100: a := []: s := 0: x := exp(1.0): for n from 1 to 1000000 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 Cf. A007677 (denominators of convergents to e), A079934, A079937, A079940.
%K more,nonn
%O 1,2
%A _Benoit Cloitre_ and _Paul D. Hanna_, Jan 21 2003
%E Two more terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 30 2003