A332013 T(n, k) is the least positive m such that floor(n/m) AND floor(k/m) = 0 (where AND denotes the bitwise AND operator). Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 5, 2, 3, 2, 1, 1, 1, 3, 3, 5, 5, 3, 3, 1, 1, 1, 2, 1, 3, 3, 6, 3, 3, 1, 2, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 2, 3, 2, 1, 3, 7, 3, 1

Offset: 0

Author

Rémy Sigrist, Feb 04 2020

Keywords

• nonn
• base
• tabl

Comments

Sierpinski gasket appears at different scales in the representation of the table (see illustration in Links section).

Examples

			Array T(n, k) begins:
  n\k|  0  1  2  3  4  5  6  7  8  9 10 11 12
  ---+---------------------------------------
    0|  1  1  1  1  1  1  1  1  1  1  1  1  1
    1|  1  2  1  2  1  2  1  2  1  2  1  2  1
    2|  1  1  3  3  1  1  3  3  1  1  3  3  1
    3|  1  2  3  4  1  2  3  3  1  2  4  4  1
    4|  1  1  1  1  5  5  3  3  1  1  1  1  3
    5|  1  2  1  2  5  6  3  3  1  2  1  2  3
    6|  1  1  3  3  3  3  7  7  1  1  4  4  3
    7|  1  2  3  3  3  3  7  8  1  2  4  4  3
    8|  1  1  1  1  1  1  1  1  9  9  5  5  3
    9|  1  2  1  2  1  2  1  2  9 10  5  5  3
   10|  1  1  3  4  1  1  4  4  5  5 11 11  3
   11|  1  2  3  4  1  2  4  4  5  5 11 12  3
   12|  1  1  1  1  3  3  3  3  3  3  3  3 13
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010 (antidiagonals 0..140)
• Rémy Sigrist, Colored representation of T(n, k) for n, k = 0..1024 (where the hue is function of T(n, k), red pixels correspond to 1's)
• Wikipedia, Sierpiński triangle

Crossrefs

Cf. A000265, A331886.

Programs

PARI

T(n,k) = for (m=1, oo, if (bitand(n\m, k\m)==0, return (m)))

Formula

T(n, k) = T(k, n).

T(n, k) = 1 iff n AND k = 0.

T(n, n) = n+1.

T(n, n+1) = A000265(n+1).