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A003986 Table T(n,k) = n OR k read by antidiagonals. 81
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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
KEYWORD
tabl,nonn,look
AUTHOR
EXTENSIONS
Name edited by Michel Marcus, Jan 17 2023
STATUS
approved

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Last modified June 21 10:15 EDT 2024. Contains 373543 sequences. (Running on oeis4.)