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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.
2
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, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 49, 51, 53, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 75, 77, 79, 81, 83, 84, 85, 86, 87, 89, 91, 93, 95, 97, 98, 99, 100
OFFSET
0,3
COMMENTS
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
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.
FORMULA
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.
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 := A
CROSSREFS
Apart from initial zero, complement of A081693. Cf. A081691.
Sequence in context: A154536 A298110 A091815 * A161346 A096515 A100586
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 02 2003
EXTENSIONS
More terms from Vladeta Jovovic, Apr 04 2003
STATUS
approved