A273823 Table read by rows: the n-th row is the list of numbers to the left of n in the natural numbers read by antidiagonals.

1, 2, 1, 3, 4, 2, 1, 5, 3, 6, 7, 4, 2, 1, 8, 5, 3, 9, 6, 10, 11, 7, 4, 2, 1, 12, 8, 5, 3, 13, 9, 6, 14, 10, 15, 16, 11, 7, 4, 2, 1, 17, 12, 8, 5, 3, 18, 13, 9, 6, 19, 14, 10, 20, 15, 21, 22, 16, 11, 7, 4, 2, 1, 23, 17, 12, 8, 5, 3, 24, 18, 13, 9, 6, 25, 19, 14

Offset: 1

Author

Peter Kagey, Jun 08 2016

Keywords

• nonn
• tabf
• look

Examples

			A000027 read by antidiagonals is:
1 2 4 7
3 5 8
6 9
...
Thus:
Row 1: []
Row 2: [1]
Row 3: []
Row 4: [2, 1]
Row 5: [3]
Row 6: []
Row 7: [4, 2, 1]
Row 8: [5, 3]
Row 9: [6]
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000027, A025581 (row length), A269526, A271439, A273824, A273825, A274079, A274080.

Programs

Haskell

a273823 n = genericIndex a273823_list (n - 1)
a273823_list = concatMap a273823_row [1..]
a273823_tabf = map a273823_row [1..]
a273823_row n
  | a_i == 0  = []
  | otherwise = a_i : a273823_row a_i where
    a_i = a271439 n

Mathematica

nn = 32; t = Table[(n^2 - n)/2 + Accumulate@ Range[n - 1, Ceiling[(Sqrt[9 + 8 nn] - 3)/2]] + 1, {n, Ceiling[(Sqrt[9 + 8 nn] - 3)/2] + 1}]; Table[Reverse@ Take[t[[#1]], #2 - 1] & @@ Flatten@ Position[t, n], {n, nn}] // Flatten (* Michael De Vlieger, Jun 10 2016 *)