

A082218


Square array in which for every k, the kth partial sums of every row and column are divisible by k. Array read by antidiagonals, alternating upwards and downwards. Each entry is the least number not already used that fits the divisibility requirement.


6



1, 3, 5, 6, 7, 2, 10, 12, 8, 4, 9, 14, 13, 16, 19, 25, 15, 37, 21, 23, 11, 20, 17, 22, 29, 26, 35, 24, 28, 36, 18, 32, 38, 44, 40, 48, 31, 56, 33, 68, 43, 50, 39, 34, 41, 27, 47, 61, 53, 57, 45, 75, 85, 93, 55, 30, 49, 65, 63, 72, 67, 88, 69, 62, 73, 51, 81, 83, 80, 70, 128, 42
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OFFSET

1,2


COMMENTS

T(i, j) must satisfy a congruence mod i and another congruence mod j. i and j are not always relatively prime, but this pair of congruences is always solvable. See the link for a proof.  David Wasserman


LINKS

Table of n, a(n) for n=1..72.
D. Wasserman, Proof


EXAMPLE

1 3 2 10 19 25...
5 7 12 16 15...
6 8 13 37...
4 14 21...
9 23...
11...
...


CROSSREFS

Cf. A082219, A082220, A082221, A082222, A082223.
Sequence in context: A076819 A181757 A181753 * A111612 A317920 A305443
Adjacent sequences: A082215 A082216 A082217 * A082219 A082220 A082221


KEYWORD

nonn,easy,tabf


AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 09 2003


EXTENSIONS

Edited and extended by David Wasserman, Aug 26 2004.


STATUS

approved



