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A080157 Greedy frac multiples of gamma: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=gamma, where "frac(y)" denotes the fractional part of y.

%I A080157 #3 May 19 2006 03:00:00
%S A080157 1,2,7,9,26,52,149,272,395,790,1185,1580,5653,10911,16169,26685,58628,
%T A080157 85313,117256,175884,559595,2179752,5420066
%N A080157 Greedy frac multiples of gamma: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=gamma, where "frac(y)" denotes the fractional part of y.
%e A080157 a(3) = 7 since frac(1x) + frac(2x) + frac(7x) < 1, while frac(1x) + frac(2x) + frac(k*x) > 1 for all k>2 and k<7.
%p A080157 Digits := 1000: a := []: s := 0: x := evalf(gamma): 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 A080157 Cf. A079938, A079939, A079940, A079941, A080142. Searching in the OEIS for "greedy frac" gives related sequences.
%K A080157 nonn
%O A080157 1,2
%A A080157 Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003