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Search: id:A003989
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| A003989 |
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Table of GCD(x,y) read by antidiagonals, where (x,y) = (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),... |
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+0
18
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| 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 2, 1, 2, 5, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 7, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 5, 3, 1, 1, 3, 5, 1, 3, 1, 1, 1, 2, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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For m<n, the maximal number of nonattacking queens that can be placed on the n by m rectangular toroidal chessboard is GCD(m,n), except in the case m=3, n=6.
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., 1994, ch. 4.
D. E. Knuth, The Art of Computer Programming, Addison-Wesley, section 4.5.2.
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LINKS
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T. D. Noe, First 100 antidiagonals of array, flattened
Grant Cairns, Queens on Non-square Tori, Electronic Journal of Combinatorics, N6, 2001.
Index entries for sequences related to lcm's
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FORMULA
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Multiplicative in both parameters with a(p^e, m) = GCD(p^e, m). David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.
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EXAMPLE
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Table begins:
1 1 1 1 1 1 ...
1 2 1 2 1 2 ...
1 1 3 1 1 3 ...
1 2 1 4 1 2 ...
1 1 1 1 5 1 ...
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CROSSREFS
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Rows, columns and diagonals: A089128, A109007, A109008, A109009, A109010, A109011, A109012, A109013, A109014, A109015.
A109004 is (0, 0) based
Cf. A003990, A003991, A050873, A054431.
A(x, y) = A075174(A004198(A075173(x), A075173(y))) = A075176(A004198(A075175(x), A075175(y))).
Antidiagonal sums are in A006579.
Sequence in context: A124060 A140194 A159923 this_sequence A091255 A135303 A036065
Adjacent sequences: A003986 A003987 A003988 this_sequence A003990 A003991 A003992
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KEYWORD
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tabl,nonn,easy,nice,mult
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AUTHOR
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Marc LeBrun (mlb(AT)well.com)
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