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 A081693 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS A. S. Fraenkel, Home Page A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004. MATHEMATICA 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 CROSSREFS Apart from initial terms, complement of A081692. Cf. A081691. Sequence in context: A032708 A282094 A084124 * A022298 A229090 A265670 Adjacent sequences:  A081690 A081691 A081692 * A081694 A081695 A081696 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 02 2003 EXTENSIONS More terms from Vladeta Jovovic, Apr 04 2003 STATUS approved

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Last modified April 13 15:23 EDT 2021. Contains 342936 sequences. (Running on oeis4.)