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

%I A080098 #38 Feb 16 2025 08:32:48
%S A080098 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,
%T A080098 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,
%U A080098 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
%N A080098 Triangle T(n,k) = n OR k, 0 <= k <= n, bitwise logical OR, read by rows.
%H A080098 Rick L. Shepherd, <a href="/A080098/b080098.txt">Rows n = 0..500 of triangle, flattened</a>
%H A080098 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OR.html">OR.</a>
%e A080098 Triangle begins:
%e A080098    0,
%e A080098    1,  1,
%e A080098    2,  3,  2,
%e A080098    3,  3,  3,  3,
%e A080098    4,  5,  6,  7,  4,
%e A080098    5,  5,  7,  7,  5,  5,
%e A080098    6,  7,  6,  7,  6,  7,  6,
%e A080098    7,  7,  7,  7,  7,  7,  7,  7,
%e A080098    8,  9, 10, 11, 12, 13, 14, 15,  8,
%e A080098    9,  9, 11, 11, 13, 13, 15, 15,  9,  9,
%e A080098   10, 11, 10, 11, 14, 15, 14, 15, 10, 11, 10,
%e A080098   ...
%t A080098 T[n_, k_] := n ~BitOr~ k;
%t A080098 Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Dec 01 2021 *)
%o A080098 (Haskell)
%o A080098 import Data.Bits ((.|.))
%o A080098 a080098 n k = n .|. k :: Int
%o A080098 a080098_row n = map (a080098 n) [0..n]
%o A080098 a080098_tabl = map a080098_row [0..]
%o A080098 -- _Reinhard Zumkeller_, Aug 03 2014, Jul 05 2012
%o A080098 (Python)
%o A080098 def T(n, k): return n | k
%o A080098 print([T(n, k) for n in range(13) for k in range(n+1)]) # _Michael S. Branicky_, Dec 01 2021
%Y A080098 Cf. A001316 (number of integers k such that T(n, k) = n in n-th row).
%Y A080098 Cf. A350093 (row sums), A003986 (array).
%Y A080098 Other triangles: A080099 (AND), A051933 (XOR), A265705 (IMPL), A102037 (CNIMPL).
%K A080098 nonn,easy,tabl,look
%O A080098 0,4
%A A080098 _Reinhard Zumkeller_, Jan 28 2003