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A082218 Square array in which for every k, the k-th 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)