A080098 Triangle T(n,k) = n OR k, 0 <= k <= n, bitwise logical OR, read by rows.

0, 1, 1, 2, 3, 2, 3, 3, 3, 3, 4, 5, 6, 7, 4, 5, 5, 7, 7, 5, 5, 6, 7, 6, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 9, 11, 11, 13, 13, 15, 15, 9, 9, 10, 11, 10, 11, 14, 15, 14, 15, 10, 11, 10, 11, 11, 11, 11, 15, 15, 15, 15, 11, 11, 11, 11, 12, 13, 14, 15, 12, 13, 14, 15, 12, 13, 14, 15, 12

Offset: 0

Author

Reinhard Zumkeller, Jan 28 2003

Keywords

• nonn
• easy
• tabl
• look

Examples

			Triangle begins:
   0,
   1,  1,
   2,  3,  2,
   3,  3,  3,  3,
   4,  5,  6,  7,  4,
   5,  5,  7,  7,  5,  5,
   6,  7,  6,  7,  6,  7,  6,
   7,  7,  7,  7,  7,  7,  7,  7,
   8,  9, 10, 11, 12, 13, 14, 15,  8,
   9,  9, 11, 11, 13, 13, 15, 15,  9,  9,
  10, 11, 10, 11, 14, 15, 14, 15, 10, 11, 10,
  ...
		

Links

• Rick L. Shepherd, Rows n = 0..500 of triangle, flattened
• Eric Weisstein's World of Mathematics, OR.

Crossrefs

Cf. A001316 (number of integers k such that T(n, k) = n in n-th row).

Cf. A350093 (row sums), A003986 (array).

Other triangles: A080099 (AND), A051933 (XOR), A265705 (IMPL), A102037 (CNIMPL).

Programs

Haskell

import Data.Bits ((.|.))
a080098 n k = n .|. k :: Int
a080098_row n = map (a080098 n) [0..n]
a080098_tabl = map a080098_row [0..]
-- Reinhard Zumkeller, Aug 03 2014, Jul 05 2012

Mathematica

T[n_, k_] := n ~BitOr~ k;
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 01 2021 *)

Python

def T(n, k): return n | k
print([T(n, k) for n in range(13) for k in range(n+1)]) # Michael S. Branicky, Dec 01 2021