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A099354 From P-positions in a certain game. 2

%I

%S 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,

%T 34,35,36,37,39,40,41,42,43,45,46,47,49,50,51,52,53,54,56,57,58,60,62,

%U 63,64,66,68,69,70,72,73,75,76,77,79,80,81,82,83,85

%N From P-positions in a certain game.

%H Nathaniel Johnston, <a href="/A099354/b099354.txt">Table of n, a(n) for n = 0..10000</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.

%F 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.

%p 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:

%p 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:

%p seq(a(n), n=0..70); # _Nathaniel Johnston_, Apr 28 2011

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Nov 16 2004

%E Edited and corrected by _Nathaniel Johnston_, Apr 28 2011

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Last modified April 10 23:13 EDT 2021. Contains 342877 sequences. (Running on oeis4.)