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A184419 Lower s-Wythoff sequence, where s=lower Wythoff sequence. Complement of A184420. 3

%I #5 Mar 30 2012 18:57:13

%S 1,3,4,5,7,9,10,12,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35,37,

%T 38,39,41,43,44,45,47,49,50,51,53,54,56,57,59,60,62,63,65,66,68,69,70,

%U 72,74,75,76,78,79,81,83,84,85,87,88,90,91,93,94,96,97,99,100,101,103,104,106,108,109,110,112,114,115,116,118,119,121,122,124,125,127,128,130,131,133,134,135,137,139,140,141,143,144,146,148

%N Lower s-Wythoff sequence, where s=lower Wythoff sequence. Complement of A184420.

%C See A184117 for the definition of lower and upper s(n)-Wythoff sequences.

%e s=(1,3,4,6,8,9,11,12,...)=A000201=lower Wythoff sequence;

%e a=(1,3,4,5,7,9,10,12,...)=A184419;

%e b=(2,6,8,11,15,18,21,24,...)=A184420.

%e Briefly: b=s+a, where a=mex="least missing".

%t mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;

%t r=(1+5^(1/2))/2;s[n_]:=Floor[r*n];a[1]=1;b[n_]:=b[n]=s[n]+a[n];

%t a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];

%t Table[s[n],{n,40}]

%t Table[a[n],{n,100}]

%t Table[b[n],{n,100}]

%Y Cf. A184117, A000201, A184420.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 13 2011

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