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A184119 Upper s(n)-Wythoff sequence, where s(n) = 2n - 1; complement of A136119.

%I A184119 #20 Sep 08 2022 08:45:55
%S A184119 2,6,9,12,16,19,23,26,30,33,36,40,43,47,50,53,57,60,64,67,70,74,77,81,
%T A184119 84,88,91,94,98,101,105,108,111,115,118,122,125,129,132,135,139,142,
%U A184119 146,149,152,156,159,163,166,170,173,176,180,183,187,190,193,197,200,204,207,210,214,217,221,224,228,231,234,238,241,245,248,251,255,258,262,265,269,272,275,279,282,286,289,292,296,299,303,306,309,313,316,320,323,327,330,333,337,340
%N A184119 Upper s(n)-Wythoff sequence, where s(n) = 2n - 1; complement of A136119.
%C A184119 See A184117 for the definition of lower and upper s(n)-Wythoff sequences.
%C A184119 (a(n)) is an inhomogeneous Beatty sequence, the complement of the inhomogeneous Beatty sequence (A136119(n)) = (floor(sqrt(2)*n + 1 - sqrt(2)/2)). See the paper by Fraenkel. - _Michel Dekking_, Jan 31 2017
%H A184119 Vincenzo Librandi, <a href="/A184119/b184119.txt">Table of n, a(n) for n = 1..2000</a>
%H A184119 Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.1090/S0002-9947-1994-1138949-9">Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups</a>, Transactions of the American Mathematical Society 341.2 (1994): p. 640.
%F A184119 a(n) = floor((2+sqrt(2))*n - sqrt(2)/2). - _Michel Dekking_, Jan 31 2017
%t A184119 k=2; r=1;
%t A184119 mex:=First[Complement[Range[1, Max[#1]+1], #1]]&;
%t A184119 s[n_]:=k*n-r; a[1]=1; b[n_]:=b[n]=s[n]+a[n];
%t A184119 a[n_]:=a[n]=mex[Flatten[Table[{a[i], b[i]},{i, 1, n-1}]]];
%t A184119 Table[s[n], {n, 30}]
%t A184119 Table[a[n], {n, 100}]
%t A184119 Table[b[n], {n, 100}]
%t A184119 Table[(Floor[(2 + Sqrt[2]) n - Sqrt[2]/2]), {n, 100}] (* _Vincenzo Librandi_, Jan 31 2017 *)
%o A184119 (Magma) [Floor((2+Sqrt(2))*n-Sqrt(2)/2): n in [1..80]]; // _Vincenzo Librandi_, Jan 31 2017
%Y A184119 Cf. A136119, A184117.
%K A184119 nonn
%O A184119 1,1
%A A184119 _Clark Kimberling_, Jan 09 2011