A079941 - OEIS

A079941

Greedy frac multiples of log(2): a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=log(2).

%I #10 Sep 02 2013 03:10:55

%S 1,3,6,13,26,39,277,642,2291,4582,6231,16402,26573,36744,63317,73488,

%T 110232,414355,828710

%N Greedy frac multiples of log(2): a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=log(2).

%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) = 13 since frac(1x) + frac(3x) + frac(6x) + frac(13x) < 1, while frac(1x) + frac(3x) + frac(6x) + frac(k*x) > 1 for all k>6 and k<13.

%Y Cf. A079943 (denominators of convergents to ln2), A079934, A079939, A079940.

%K nonn

%O 1,2

%A _Benoit Cloitre_ and _Paul D. Hanna_, Jan 21 2003

%E More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003