A082017 -id:A082017 - cp's OEIS frontend

A074135 Triangle read by rows: for 1 <= k < n, a(n, k) is the least positive integer not already used. a(n, n) is the least positive integer not already used that makes the row sum a multiple of n.

1, 2, 4, 3, 5, 7, 6, 8, 9, 13, 10, 11, 12, 14, 18, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 36, 37, 38, 39, 41, 42, 43, 44, 49, 45, 46, 47, 48, 50, 51, 52, 53, 54, 64, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 75, 66, 67, 68, 69, 70, 71

Offset: 1

Amarnath Murthy, Aug 27 2002

Alternative (but equivalent) definition: In the following square array, numbers (not occurring earlier) are entered like this a(1, 1), a(1, 2), a(2, 1), a(3, 1), a(2, 2), a(1, 3), a(1, 4), a(2, 3), a(3, 2), a(4, 1), a(5, 1), a(4, 2), ... such that the n-th diagonal sum is a multiple of n. 1 2 7 6 18... 4 5 8 14... 3 9 12... 13 11... 10... ... sequence contains terms as they are entered.

Cf. A074132, A074133, A074134, A074136.

Cf. A082017, A082018, A082019, A082020.

Edited and extended by David Wasserman, Oct 31 2006

Further edited by N. J. A. Sloane Jan 17 2009 at the suggestion of R. J. Mathar

A082018 First column of square array T(n,k) with T(1,1) = 1 where antidiagonals are filled alternating upwards and downwards with the smallest number not already used such that the n-th antidiagonal sum is a multiple of n.

Original entry on oeis.org

1, 4, 3, 13, 10, 21, 22, 40, 36, 64, 55, 81, 78, 115, 105, 138, 136, 182, 171, 211, 210, 265, 253, 300, 301, 364, 351, 433, 406, 477, 465, 556, 528, 606, 595, 695, 666, 751, 741, 850, 820, 912, 903, 1021, 990, 1089, 1081, 1208, 1176, 1282, 1275, 1411, 1378

Offset: 1

Amarnath Murthy, Apr 05 2003

nonn

This is the boustrophedon method of filling an array. Sums of antidiagonals of T are in A074132. Sums of antidiagonals of T divided by number of antidiagonals are in A074133. Diagonal of T is in A082019.

			T(n,k) begins:
1,   2,  7,  6, 18, 15, ...
4,   5,  8, 14, 16, 27, ...
3,   9, 12, 17, 26, 31, ...
13, 11, 19, 25, 32, 42, ...
10, 20, 24, 33, 41, 50, ...
21, 23, 34, 39, 51, 60, ...

Cf. A074135, A082017, A082019, A082020, A082002, A082003, A082004, A082005.

Edited and more terms from Alois P. Heinz, Oct 26 2011

A082019 Diagonal of square array T(n,k) with T(1,1) = 1 where antidiagonals are filled alternating upwards and downwards with the smallest number not already used such that the n-th antidiagonal sum is a multiple of n.

Original entry on oeis.org

1, 5, 12, 25, 41, 60, 85, 112, 145, 180, 221, 264, 313, 365, 420, 481, 544, 613, 684, 761, 840, 925, 1012, 1105, 1200, 1301, 1404, 1513, 1624, 1741, 1860, 1985, 2112, 2245, 2380, 2521, 2664, 2813, 2964, 3121, 3281, 3444, 3613, 3784, 3961, 4140, 4325, 4512

Offset: 1

Amarnath Murthy, Apr 05 2003

nonn

			T(n,k) begins:
1,   2,  7,  6, 18, 15, ...
4,   5,  8, 14, 16, 27, ...
3,   9, 12, 17, 26, 31, ...
13, 11, 19, 25, 32, 42, ...
10, 20, 24, 33, 41, 50, ...
21, 23, 34, 39, 51, 60, ...

Cf. A074135, A082017, A082018, A082002, A082003, A082004, A082005.

Edited and more terms from Alois P. Heinz, Oct 26 2011

cp's OEIS Frontend

A074135 Triangle read by rows: for 1 <= k < n, a(n, k) is the least positive integer not already used. a(n, n) is the least positive integer not already used that makes the row sum a multiple of n.

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A082018 First column of square array T(n,k) with T(1,1) = 1 where antidiagonals are filled alternating upwards and downwards with the smallest number not already used such that the n-th antidiagonal sum is a multiple of n.

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A082019 Diagonal of square array T(n,k) with T(1,1) = 1 where antidiagonals are filled alternating upwards and downwards with the smallest number not already used such that the n-th antidiagonal sum is a multiple of n.

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Author

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Examples

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