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%I #30 Jan 11 2022 12:35:30
%S 0,2,4,1,3,8,10,12,14,5,7,18,6,21,9,24,26,28,30,11,13,34,36,38,40,15,
%T 17,44,16,47,19,50,52,20,55,57,59,22,62,23,65,27,25,69,71,73,75,77,29,
%U 31,81,83,85,32,88,33,91,37,35,95,97,99,101,39,104,106,41,109,42,112,43,115,117,119,45,122
%N "Greedy Queens" permutation of the nonnegative integers.
%C This permutation is produced by a simple greedy algorithm: starting from the top left corner of an infinite chessboard placed in the fourth quadrant of the plane, walk along successive antidiagonals and place a queen in the first available position where it is not threatened by any of the existing queens. In other words, this permutation satisfies the condition that p(i+d) <> p(i)+-d for all i and d >= 1.
%C The rows and columns are indexed starting at 0. p(n) = k means that a queen appears in column n in row k. - _N. J. A. Sloane_, Aug 18 2016
%C All of A065188 (same for positive integers), A065189, A199134, A275884 should really have started at 0 rather than 1. Then the graph of A065188, for example, would be comparable with the graph of A002251.
%C That this is a permutation of the nonnegative integers follows from the proof in A269526 that every row and every column in that array is a permutation of the positive integers. In particular, every row and every column contains a 0 (which translates to a queen in the present sequence). - _N. J. A. Sloane_, Dec 10 2017
%H N. J. A. Sloane, <a href="/A275895/b275895.txt">Table of n, a(n) for n = 0..9999</a>
%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://doi.org/10.37236/8905">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.
%H N. J. A. Sloane, <a href="/A275895/a275895.txt">Table of n, a(n) for n = 0..49999</a>
%F a(n) = A065188(n+1)-1.
%Y Cf. A065188 (same for positive integers), A065189 (it's inverse), A199134 (indices of a(n) < n), A275884 (complement), A275894 (same for "nonnegative", i.e., this sequence), A275896 (same for A065189), A002251 (Wythoff pairs).
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Aug 23 2016
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