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.

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

Author

N. J. A. Sloane, Apr 02 2003

Keywords

• nonn

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.

Crossrefs

Apart from initial zero, complement of A081693. Cf. A081691.

Programs

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

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.

Extensions

More terms from Vladeta Jovovic, Apr 04 2003