A003986 Table T(n,k) = n OR k read by antidiagonals.

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

Offset

0,4

Links

T. D. Noe, Rows n=0..100 of triangle, flattened

Formula

T(x,y) = T(y,x) = A080098(x,y). - R. J. Mathar, May 28 2011

Example

The upper left corner of the array starts in row x=0 with columns y>=0 as:
   0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, ...
   1,  1,  3,  3,  5,  5,  7,  7,  9,  9, 11, 11, 13, ...
   2,  3,  2,  3,  6,  7,  6,  7, 10, 11, 10, 11, 14, ...
   3,  3,  3,  3,  7,  7,  7,  7, 11, 11, 11, 11, 15, ...
   4,  5,  6,  7,  4,  5,  6,  7, 12, 13, 14, 15, 12, ...
   5,  5,  7,  7,  5,  5,  7,  7, 13, 13, 15, 15, 13, ...
   6,  7,  6,  7,  6,  7,  6,  7, 14, 15, 14, 15, 14, ...
   7,  7,  7,  7,  7,  7,  7,  7, 15, 15, 15, 15, 15, ...
   8,  9, 10, 11, 12, 13, 14, 15,  8,  9, 10, 11, 12, ...
   9,  9, 11, 11, 13, 13, 15, 15,  9,  9, 11, 11, 13, ...
  10, 11, 10, 11, 14, 15, 14, 15, 10, 11, 10, 11, 14, ...

Maple

read("transforms") ;
A003986 := proc(x, y) ORnos(x, y) ; end proc:
for d from 0 to 12 do for x from 0 to d do printf("%d, ", A003986(x, d-x)) ; end do: end do: # R. J. Mathar, May 28 2011

Mathematica

Table[BitOr[k, n - k], {n, 0, 20}, {k, 0, n}] //Flatten (* Indranil Ghosh, Apr 01 2017 *)

Prog

(Haskell)
import Data.Bits ((.|.))
a003986 n k = (n - k) .|. k :: Int
a003986_row n = map (a003986 n) [0..n]
a003986_tabl = map a003986_row [0..]
-- Reinhard Zumkeller, Aug 05 2014
(PARI)
tabl(nn) = {for(n=0, nn, for(k=0, n, print1(bitor(k, n - k), ", "); ); print(); ); };
tabl(20) \\ Indranil Ghosh, Apr 01 2017
(Python)
for n in range(21):
    print([k|(n - k) for k in range(n + 1)])
# Indranil Ghosh, Apr 01 2017
(C)
#include <stdio.h>
int main()
{
int n, k;
for (n=0; n<=20; n++){
    for(k=0; k<=n; k++){
        printf("%d, ", (k|(n - k)));
    }
    printf("\n");
}
return 0;
} /* Indranil Ghosh, Apr 01 2017 */

Crossrefs

Cf. A003987 (XOR) and A004198 (AND). Cf. also A075173, A075175.

Antidiagonal sums are in A006583.

Sequence in context: A361789 A343040 A343044 * A343836 A123603 A228506

Adjacent sequences: A003983 A003984 A003985 * A003987 A003988 A003989

Keyword

tabl,nonn,look

Author

Marc LeBrun

Extensions

Name edited by Michel Marcus, Jan 17 2023

Status

approved