A233208 - OEIS

%I #16 Dec 13 2013 05:01:30

%S 3,2,6,7,2,3,35,3,2,5,10,2,2,17,4,2,4,14,2,2,11,5,2,4,23,3,2,8,5,2,3,

%T 66,3,2,7,7,2,3,76,3,2,5,8,2,3,24,4,2,5,11,2,2,14,4,2,4,17,2,2,10,5,2,

%U 3,33,3,2,8,6,2,3,502,3,2,6,7,2,3,38,3,2,5,9,2,2,18,4,2,4,13,2,2,12,5,2,4,22

%N A measure of quality (the higher the better) for the approximation to e by rationals A022852(n)/n.

%C a(n) is the greatest natural number such that abs( n*e-A022852(n) ) < 1/a(n). Trivially a(n)>=2. a(n)=2 iff n is in A191104 (easy proof).

%F a(n) = floor( 1 / abs( n*e-A022852(n) ) ).

%e a(7) = 35 because floor(1/abs(7*e-19)) = floor(1/0.0279727...) = floor(35.749...) = 35.

%o (PARI) a(n)=floor(1/abs(n*exp(1)-round(n*exp(1)))) \\ _Ralf Stephan_, Dec 13 2013

%Y Cf. A022852. For records see A233209, A007677.

%K nonn

%O 1,1

%A _Franz Vrabec_, Dec 06 2013

%E More terms from _Ralf Stephan_, Dec 13 2013