A097286 Rectangular array T by descending antidiagonals: T(n,k) = rank of k-th n in A097285.

1, 3, 2, 7, 5, 4, 13, 9, 6, 8, 21, 15, 11, 10, 14, 31, 23, 17, 12, 16, 22, 43, 33, 25, 19, 18, 24, 32, 57, 45, 35, 27, 20, 26, 34, 44, 73, 59, 47, 37, 29, 28, 36, 46, 58, 91, 75, 61, 49, 39, 30, 38, 48, 60, 74, 111, 93, 77, 63, 51, 41, 40, 50, 62, 76, 92, 133, 113, 95, 79, 65, 53, 42, 52, 64, 78, 94, 112

Offset: 1

Author

Clark Kimberling, Aug 05 2004

Keywords

• nonn
• tabl

Comments

As a sequence, this is a permutation of the natural numbers.

Examples

			Corner:
   1    3    7   13    21    31    43    57    73    91   111
   2    5    9   15    23    33    45    59    75    93   113
   4    6   11   17    25    35    47    61    77    95   115
   8   10   12   19    27    37    49    63    79    97   117
  14   16   18   20    29    39    51    65    81    99   119
  22   24   26   28    30    41    53    67    83   101   121
  32   34   36   38    40    42    55    69    85   103   123
  44   46   48   50    52    54    56    71    87   105   125
  58   60   62   64    66    68    70    72    89   107   127
  74   76   78   80    82    84    86    88    90   109   129
  92   94   96   98   100   102   104   106   108   110   131
		

Crossrefs

Cf. A002061 (row 1), A014206 (column 1), A097285.

Programs

Mathematica

s = {1, 2}; Do[s = Join[s, Riffle[Range[n - 1], n], {n}], {n, 3, 12}];
Grid[Table[Flatten[Position[s, n]], {n, 1, 12}]]  (* Clark Kimberling, May 09 2025 *)