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%I #14 Apr 14 2017 03:55:28
%S 0,2,8,10,12,14,16,22,28,34,40,46,48,50,52,54,60,62,64,66,68,74,76,78,
%T 80,82,88,90,92,94,96,102,104,106,108,110,116,122,128,134,140,142,144,
%U 146,148,154,160,166,172,178,180,182,184,186,192,198,204,210,216,218
%N 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.
%C 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
%H A. S. Fraenkel, <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/">Home Page</a>
%H 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.
%t 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
%Y Apart from initial terms, complement of A081692. Cf. A081691.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Apr 02 2003
%E More terms from _Vladeta Jovovic_, Apr 04 2003
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