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A045672
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Extension of Beatty sequence; complement of A045671 (apart from the initial 0).
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6
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0, 4, 8, 12, 18, 22, 26, 32, 36, 40, 46, 50, 54, 58, 62, 68, 72, 76, 82, 86, 90, 96, 100, 104, 108, 112, 118, 122, 126, 132, 136, 140, 146, 150, 154, 158, 162, 168, 172, 176, 182, 186, 190, 196, 200, 204, 210, 214, 218, 224, 228, 232, 236, 240, 246, 250
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OFFSET
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0,2
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COMMENTS
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(s,t)-sequences; the case s=2, t=2.
The sequence can also be characterized by a special numeration system-see above reference.
For n>=1, these are the positions of 0 in the fixed point of the morphism 0->11, 1->1110; see A285671 and Mathematica program. Conjecture: -1 < n*r - a(n) < 3 for n>=0, where r = (5 + sqrt(17))/2. - Clark Kimberling, May 02 2017
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LINKS
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FORMULA
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MATHEMATICA
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s=2; t=2;
mex:=First[Complement[Range[1, Max[#1]+1], #1]]&;
a[0]=0; b[n_]:=b[n]=s*a[n]+t*n;
a[n_]:=a[n]=mex[Flatten[Table[{a[i], b[i]}, {i, 0, n-1}]]];
Table[a[n], {n, 200}] (* A045671 *)
Table[b[n], {n, 200}] (* A045672 *)
s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 1, 0}}] &, {0}, 10]; (* A285671 *)
Flatten[Position[s, 0]]; (* A045672 *)
Flatten[Position[s, 1]]; (* A045671 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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