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A184478 Lower s-Wythoff sequence, where s(n) = 3n + 1. Complement of A184479.

%I A184478 #16 Sep 08 2022 08:45:55
%S A184478 1,2,3,4,6,7,8,10,11,12,14,15,16,18,19,20,21,23,24,25,27,28,29,31,32,
%T A184478 33,34,36,37,38,40,41,42,44,45,46,47,49,50,51,53,54,55,57,58,59,60,62,
%U A184478 63,64,66,67,68,70,71,72,74,75,76,77,79,80,81,83,84,85,87,88,89,90,92,93,94,96,97,98,100,101,102,103,105,106,107,109,110,111,113,114,115,117,118,119,120,122,123,124,126,127,128,130,131,132,133,135,136,137,139,140,141,143,144,145,146,148,149,150,152,153,154,156
%N A184478 Lower s-Wythoff sequence, where s(n) = 3n + 1.  Complement of A184479.
%C A184478 See A184117 for the definition of lower and upper s-Wythoff sequences.
%C A184478 The sequence is defined by a(1) = 1 and for n > 1, a(n) is the smallest positive integer not in {a(k), a(k) + s(k); k < n}. - _M. F. Hasler_, Jan 07 2019
%F A184478 a(n) = A184479(n) - s(n). - _M. F. Hasler_, Jan 07 2019
%p A184478 a:=n->floor(n*(-1+sqrt(13))/2+1): seq(a(n),n=0..120); # _Muniru A Asiru_, Jan 08 2019
%t A184478 k=3; r=-1; d=Sqrt[4+k^2];
%t A184478 a[n_]:=Floor[(1/2)(d+2-k)(n+r/(d+2))];
%t A184478 b[n_]:=Floor[(1/2)(d+2+k)(n-r/(d+2))];
%t A184478 Table[a[n],{n,120}]
%t A184478 Table[b[n],{n,120}]
%t A184478 Table[(Floor[n (-1 + Sqrt[13]) / 2]) + 1, {n, 0, 120}] (* _Vincenzo Librandi_, Jan 08 2019 *)
%o A184478 (PARI) A184478_upto(N, s(n)=3*n+1, a=[1], U=a)={while(a[#a]<N, U=setunion(U, [a[#a], a[#a]+s(#a)]); while(#U>1&&U[2]==U[1]+1, U=U[^1]); a=concat(a, U[1]+1)); a} \\ _M. F. Hasler_, Jan 07 2019
%o A184478 (Magma) [(Floor(n*(-1+Sqrt(13))/2))+1: n in [0..120]]; // _Vincenzo Librandi_, Jan 08 2019
%Y A184478 Cf. A184117, A184479, A184480.
%K A184478 nonn
%O A184478 1,2
%A A184478 _Clark Kimberling_, Jan 15 2011