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A081692 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 A_n. B_n is in A081693.

%I A081692 #18 Dec 02 2019 06:14:43
%S A081692 0,1,3,4,5,6,7,9,11,13,15,17,18,19,20,21,23,24,25,26,27,29,30,31,32,
%T A081692 33,35,36,37,38,39,41,42,43,44,45,47,49,51,53,55,56,57,58,59,61,63,65,
%U A081692 67,69,70,71,72,73,75,77,79,81,83,84,85,86,87,89,91,93,95,97,98,99,100
%N A081692 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 A_n. B_n is in A081693.
%C A081692 Conjecture: Except for the initial 0, this is the sequence of positions of 0 in the fixed point of the morphism 0->01, 1->0000; see A284683. - _Clark Kimberling_, Apr 13 2017
%H A081692 A. S. Fraenkel, <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/">Home Page</a>
%H A081692 A. S. Fraenkel, <a href="http://www.emis.de/journals/INTEGERS/papers/eg6/eg6.Abstract.html">New games related to old and new sequences</a>, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.
%F A081692 Let a(n) = this sequence, b(n) = A081691. Then a(n) = mex{ a(i), b(i) : 0 <= i < n}, b(0) = 0, b(n) = 2(b(n-1) - a(n-1)) + a(n) + 1.
%t A081692 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 := A
%Y A081692 Apart from initial zero, complement of A081693. Cf. A081691.
%K A081692 nonn
%O A081692 0,3
%A A081692 _N. J. A. Sloane_, Apr 02 2003
%E A081692 More terms from _Vladeta Jovovic_, Apr 04 2003