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

Author

Marc LeBrun

Keywords

• tabl
• nonn
• look

Examples

			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, ...
		

Links

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

Crossrefs

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

Antidiagonal sums are in A006583.

Programs

C

#include 
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 */

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

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 *)

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

Formula

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

Extensions

Name edited by Michel Marcus, Jan 17 2023