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

1,2

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.

Links

Table of n, a(n) for n=1..92.

Formula

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

Example

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.

Sequence in context: A305296 A114544 A154726 * A244929 A302920 A280386

Adjacent sequences: A325781 A325782 A325783 * A325785 A325786 A325787

Keyword

nonn,tabl

Author

Eric Angelini, May 21 2019

Status

approved