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A184618 a(n) = floor(n*r + h), where r=sqrt(2) and h=1/3; complement of A184619.

%I A184618 #17 Sep 08 2022 08:45:55
%S A184618 1,3,4,5,7,8,10,11,13,14,15,17,18,20,21,22,24,25,27,28,30,31,32,34,35,
%T A184618 37,38,39,41,42,44,45,47,48,49,51,52,54,55,56,58,59,61,62,63,65,66,68,
%U A184618 69,71,72,73,75,76,78,79,80,82,83,85,86,88,89,90,92,93,95,96,97
%N A184618 a(n) = floor(n*r + h), where r=sqrt(2) and h=1/3; complement of A184619.
%C A184618 Sequences of the form (floor(n*r + h)) are sometimes called nonhomogeneous Beatty sequences when h is not zero.
%H A184618 Vincenzo Librandi, <a href="/A184618/b184618.txt">Table of n, a(n) for n = 1..10000</a>
%F A184618 a(n) = floor(n*r + h), where r=sqrt(2), h=1/3.
%t A184618 r=2^(1/2); h=1/3; s=r/(r-1);
%t A184618 Table[Floor[n*r+h],{n,1,120}]  (* A184618 *)
%t A184618 Table[Floor[n*s+h-h*s],{n,1,120}]  (* A184619 *)
%o A184618 (Magma) [Floor(n*Sqrt(2)+1/3): n in [1..80]]; // _Vincenzo Librandi_, Jul 07 2011
%o A184618 (PARI) a(n)=floor(n*sqrt(2)+1/3) \\ _Charles R Greathouse IV_, Jul 07 2011
%Y A184618 Cf. A184619.
%K A184618 nonn
%O A184618 1,2
%A A184618 _Clark Kimberling_, Jan 18 2011