A325784 Reading the first row of this array or its successive antidiagonals is the same as reading this sequence.

1, 2, 3, 3, 4, 5, 3, 6, 7, 8, 4, 9, 10, 11, 12, 5, 13, 14, 15, 16, 17, 3, 18, 19, 20, 21, 22, 23, 6, 24, 25, 26, 27, 28, 29, 30, 7, 31, 32, 33, 34, 35, 36, 37, 38, 8, 39, 40, 41, 42, 43, 44, 45, 46, 47, 4, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 9, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 10, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 11

Offset: 1

Author

Eric Angelini, May 21 2019

Keywords

• nonn
• tabl

Comments

The array is always extended by its antidiagonals with the smallest term not yet present that doesn't lead to a contradiction. The sequence is thus the lexicographically earliest of its kind.

Examples

			Array:
   1  2  3  3   4   5   3   6   7   8   4 ...
   3  4  6  9  13  18  24  31  39  48  58 ...
   5  7 10 14  19  25  32  40  49  59  70 ...
   8 11 15 20  26  33  41  50  60  71  83 ...
  12 16 21 27  34  42  51  61  72  84  97 ...
  17 22 28 35  43  52  62  73  85  98 112 ...
  23 29 36 44  53  63  74  86  99 113 128 ...
  30 37 45 54  64  75  87 100 114 129 145 ...
  38 46 55 65  76  88 101 115 130 146 163 ...
  47 56 66 77  89 102 116 131 147 164 182 ...
  57 67 78 90 103 117 132 148 165 183 202 ...
  ...
		

Crossrefs

Cf. A325783 and A325785 where the same idea is developed.

Cf. A000124.

Formula

a(n*(n-1)/2 + 1) = a(n). - Rémy Sigrist, May 21 2019