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

0,4

Links

Rick L. Shepherd, Rows n = 0..500 of triangle, flattened

Eric Weisstein's World of Mathematics, OR.

Example

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,
  ...

Mathematica

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

Prog

(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
(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

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).

Sequence in context: A346153 A266119 A026263 * A083060 A346643 A272979

Adjacent sequences: A080095 A080096 A080097 * A080099 A080100 A080101

Keyword

nonn,easy,tabl,look

Author

Reinhard Zumkeller, Jan 28 2003

Status

approved