A099354 From P-positions in a certain game.

0, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 32, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 81, 82, 83, 85

Offset: 0

Author

N. J. A. Sloane, Nov 16 2004

Keywords

• nonn
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000
• A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

Programs

Maple

a:=proc(n) option remember: local j, t: if(n=0)then return 0: else t:=a(n-1)+1: for j from 0 to n-1 do if(t=b(j))then return t+1: elif(tNathaniel Johnston, Apr 28 2011

Formula

Let a(n) = this sequence, b(n) = A099355. Then a(n) = the smallest number not in {a(0), b(0), a(1), b(1), ..., a(n-1), b(n-1)}; b(n) = b(n-1) - a(n-1) + a(n) + (-1)^b(n-1) - (-1)^a(n-1) + 3. Apart from initial zero, complement of A099355.

Extensions

Edited and corrected by Nathaniel Johnston, Apr 28 2011