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A081693
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Define two sequences by A_n = mex{A_i,B_i : 0 <= i < n}, B_n = B_{n-1} + (A_n-A_{n-1})(A_n-A_{n-1}+1), where the mex of a set is the smallest nonnegative integer not in the set. Sequence gives B_n. A_n is in A081692.
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2
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0, 2, 8, 10, 12, 14, 16, 22, 28, 34, 40, 46, 48, 50, 52, 54, 60, 62, 64, 66, 68, 74, 76, 78, 80, 82, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 116, 122, 128, 134, 140, 142, 144, 146, 148, 154, 160, 166, 172, 178, 180, 182, 184, 186, 192, 198, 204, 210, 216, 218
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OFFSET
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0,2
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COMMENTS
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Conjecture: Except for the initial 0, this is the sequence of positions of 1 in the fixed point of the morphism 0->01, 1->0000; see A284683. - Clark Kimberling, April 13 2017
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LINKS
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MATHEMATICA
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mex[{}]=0; mex[s_] := Complement[Range[0, 1+Max@@s], s][[1]]; A[0]=B[0]=0; A[n_] := A[n]=mex[Flatten[Table[{A[i], B[i]}, {i, 0, n-1}]]]; B[n_] := B[n]=B[n-1]+(A[n]-A[n-1])*(A[n]-A[n-1]+1); a := B
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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