A331886 -id:A331886 - cp's OEIS frontend

A331902 T(n, k) = floor(n/m) where m is the least positive integer such that floor(n/m) = floor(k/m). Square array read by antidiagonals, for n >= 0 and k >= 0.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0

Offset: 0

Rémy Sigrist, Jan 31 2020

For any n > 0, the n-th row has A001651(n) nonzero terms.

			Array T(n, k) begins (with dots instead of 0's for readability):
   n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
   ---+----------------------------------------------------
     0|   .   .   .   .   .   .   .   .   .   .   .   .   .
     1|   .   1   .   .   .   .   .   .   .   .   .   .   .
     2|   .   .   2   1   .   .   .   .   .   .   .   .   .
     3|   .   .   1   3   1   1   .   .   .   .   .   .   .
     4|   .   .   .   1   4   2   1   1   .   .   .   .   .
     5|   .   .   .   1   2   5   1   1   1   1   .   .   .
     6|   .   .   .   .   1   1   6   3   2   1   1   1   .
     7|   .   .   .   .   1   1   3   7   2   1   1   1   1
     8|   .   .   .   .   .   1   2   2   8   4   2   2   1
     9|   .   .   .   .   .   1   1   1   4   9   3   3   1
    10|   .   .   .   .   .   .   1   1   2   3  10   5   2
    11|   .   .   .   .   .   .   1   1   2   3   5  11   2
    12|   .   .   .   .   .   .   .   1   1   1   2   2  12

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..1000 (where the hue is function of T(n, k), red pixels correspond to 0's)

Cf. A001651, A213633, A331886.

T(n,k) = for (x=1, oo, if (n\x==k\x, return (n\x)))

T(n, k) = floor(n/A331886(n, k)) = floor(k/A331886(n, k)).
T(n, k) = T(k, n).
T(n, k) = 0 iff max(n, k) >= 2*min(n, k).
T(n, n+1) = A213633(n+1).

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.

Original entry on oeis.org

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

Rémy Sigrist, Feb 04 2020

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

			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

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

Cf. A000265, A331886.

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

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).

cp's OEIS Frontend

A331902 T(n, k) = floor(n/m) where m is the least positive integer such that floor(n/m) = floor(k/m). Square array read by antidiagonals, for n >= 0 and k >= 0.

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