|
|
A275895
|
|
"Greedy Queens" permutation of the nonnegative integers.
|
|
7
|
|
|
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, 17, 44, 16, 47, 19, 50, 52, 20, 55, 57, 59, 22, 62, 23, 65, 27, 25, 69, 71, 73, 75, 77, 29, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
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.
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
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
|
|
LINKS
|
|
|
FORMULA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|