A099356 - OEIS

%I #10 Nov 23 2014 03:43:13

%S 0,1,3,4,6,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,

%T 29,30,31,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,54,

%U 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69

%N From P-positions in a certain game.

%H Nathaniel Johnston, <a href="/A099356/b099356.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) = A099357. 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) + (-1)^a(n-1)*a(n-1) + a(n) + 1. Apart from initial zero, complement of A099357.

%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) + (-1)^a(n-1)*a(n-1) + a(n) + 1: fi: end:

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

%Y Cf. A099352 - A099355.

%K nonn,easy

%O 0,3

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