A097292 -id:A097292 - cp's OEIS frontend

A269780 Table read by antidiagonals where T(i,j) is the location of the pair (i,j) in A269501.

1, 2, 4, 5, 3, 9, 10, 8, 7, 16, 17, 15, 6, 14, 25, 26, 24, 13, 12, 23, 36, 37, 35, 22, 11, 21, 34, 49, 50, 48, 33, 20, 19, 32, 47, 64, 65, 63, 46, 31, 18, 30, 45, 62, 81, 82, 80, 61, 44, 29, 28, 43, 60, 79, 100, 101, 99, 78, 59, 42, 27, 41, 58, 77, 98, 121, 122, 120, 97, 76, 57, 40, 39, 56, 75, 96, 119, 144

Offset: 1

Franklin T. Adams-Watters, Mar 04 2016

This is trivially a permutation of the positive integers.

The "location" of the pair is taken to be the index of the second element of the pair.

			The table starts:
   1,  2,  5, 10, 17, 26
   4,  3,  8, 15, 24, 35
   9,  7,  6, 13, 22, 33
  16, 14, 12, 11, 20, 31
  25, 23, 21, 19, 18, 29
  36, 34, 32, 30, 28, 27

Cf. A269501, A097292, A002522 (top row, left shifted).

If 1 is subtracted from each term we get A316323.

T(i,j) :=
   if i=1, then (j-1)^2 + 1,
   if i>j, then i^2 - 2j + 2,
   and otherwise j^2 - 2i + 3.

A097347 Rectangular array, by antidiagonals: T(n,k) = rank of k-th n in A097291.

Original entry on oeis.org

1, 2, 3, 5, 4, 6, 10, 8, 7, 11, 17, 13, 9, 12, 18, 26, 20, 15, 14, 19, 27, 37, 29, 22, 16, 21, 28, 38, 50, 40, 31, 24, 23, 30, 39, 51, 65, 53, 42, 33, 25, 32, 41, 52, 66, 82, 68, 55, 44, 35, 34, 43, 54, 67, 83, 101, 85, 70, 57, 46, 36, 45, 56, 69, 84, 102, 122, 104, 87, 72, 59

Offset: 1

Clark Kimberling, Aug 06 2004

As a sequence, this is a permutation of the natural numbers. Row 1 is A002522 (n^2 + 1); main diagonal is A000290 (n^2); column 1 is A010000 (n^2 + 2).

			Northwest corner:
1 2 5 10
3 4 8 13
6 7 9 15
11 12 14 16

Cf. A097291, A097292.

cp's OEIS Frontend

A269780 Table read by antidiagonals where T(i,j) is the location of the pair (i,j) in A269501.

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