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

0,3

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.

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.

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(t<b(j))then break: fi: od: return t: fi: end:
b:=proc(n) option remember: if(n=0)then return 0: else return b(n-1) - a(n-1) + a(n) + (-1)^b(n-1) - (-1)^a(n-1) + 3: fi: end:
seq(a(n), n=0..70); # Nathaniel Johnston, Apr 28 2011

Crossrefs

Sequence in context: A360556 A039194 A242485 * A039115 A285964 A198045

Adjacent sequences: A099351 A099352 A099353 * A099355 A099356 A099357

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 16 2004

Extensions

Edited and corrected by Nathaniel Johnston, Apr 28 2011

Status

approved