%I #23 Jan 04 2016 01:56:36
%S 1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35,36,
%T 38,39,41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,63,65,66,68,69,71,
%U 72,73,75,76,78,79,81,82,84,85,87,88,90,91,93,94,96,97,99,100,102,103
%N Beatty sequence for (e^2 + 1)/(e^2 - e + 1).
%H Harry J. Smith, <a href="/A059564/b059564.txt">Table of n, a(n) for n = 1..2000</a>
%H Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, <a href="http://dx.doi.org/10.1016/0012-365X(72)90012-X">Characterization of the set of values f(n)=[n alpha], n=1,2,...</a>, Discrete Math. 2 (1972), no.4, 335-345.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F a(n) = floor(n*(e^2+1)/(e^2-e+1)). - _Michel Marcus_, Jan 05 2015
%p A059564:=n->floor(n*(exp(1)^2+1)/(exp(1)^2-exp(1)+1)): seq(A059564(n), n=1..100); # _Wesley Ivan Hurt_, Jan 03 2016
%t Table[Floor[n (E^2 + 1)/(E^2 - E + 1)], {n, 80}] (* _Wesley Ivan Hurt_, Jan 03 2016 *)
%o (PARI) { default(realprecision, 100); e=exp(1); b=(e^2 + 1)/(e^2 - e + 1); for (n = 1, 2000, write("b059564.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 28 2009
%Y Beatty complement is A059563.
%K nonn,easy
%O 1,2
%A _Mitch Harris_, Jan 22 2001