A273825 Table read by rows: the n-th row is the list of numbers diagonally up and to the left of n in the natural numbers read by antidiagonals.

1, 2, 3, 4, 5, 1, 6, 7, 8, 2, 9, 3, 10, 11, 12, 4, 13, 5, 1, 14, 6, 15, 16, 17, 7, 18, 8, 2, 19, 9, 3, 20, 10, 21, 22, 23, 11, 24, 12, 4, 25, 13, 5, 1, 26, 14, 6, 27, 15, 28, 29, 30, 16, 31, 17, 7, 32, 18, 8, 2, 33, 19, 9, 3, 34, 20, 10, 35, 21, 36, 37, 38, 22

Offset: 1

Author

Peter Kagey, Jun 08 2016

Keywords

• nonn
• tabf

Examples

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

Links

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

Crossrefs

Cf. A000027, A269526, A271439, A273823, A273824, A274079, A274080.

Programs

Haskell

a273825 n = genericIndex a273825_list (n - 1)
a273825_list = concatMap a273825_row [1..]
a273825_tabf = map a273825_row [1..]
a273825_row n
  | a_i == 0  = []
  | otherwise = a_i : a273825_row a_i where
    a_i = a271439 $ a271439 (n - 1)

Mathematica

nn = 58; 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[Rest@ Map[t[[#1, #2]] & @@ # &, Most@ NestWhileList[# - 1 &, #, ! MemberQ[#, 0] &]] &@ First@ Position[t, n], {n, nn}] // Flatten (* Michael De Vlieger, Jun 29 2016 *)