A359887 Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of the unique rational q such that for any m, floor(2^m/n) AND floor(2^m/k) = floor(q*2^m) (where AND denotes the bitwise AND operator); see A359888 for the denominators.

1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 5, 0, 57, 1, 57, 0, 5, 0, 0, 0, 0, 1, 0, 1, 8, 8, 1, 0, 1, 0, 0, 0, 0, 85, 0, 37, 1, 1, 1, 37, 0, 85, 0, 0

Offset: 1

Author

Rémy Sigrist, Jan 17 2023

Keywords

• nonn
• base
• frac
• tabf

Comments

A(n, k)/A359888(n, k) can be interpreted as (1/n) AND (1/k) (assuming that inverses of powers of 2 have terminating binary expansions).

Examples

			Square array A(n, k) begins:
  n\k | 1  2   3  4    5  6     7  8       9   10      11  12
  ----+------------------------------------------------------
    1 | 1  0   0  0    0  0     0  0       0    0       0   0
    2 | 0  1   0  0    0  0     0  0       0    0       0   0
    3 | 0  0   1  1    1  0     1  0       5    1      85   1
    4 | 0  0   1  1    0  0     0  0       0    0       0   0
    5 | 0  0   1  0    1  2    57  1      37    1     837   1
    6 | 0  0   0  0    2  1     8  1       2    1       8   0
    7 | 0  0   1  0   57  8     1  1       1    1    1195   1
    8 | 0  0   0  0    1  1     1  1       0    0       0   0
    9 | 0  0   5  0   37  2     1  0       1   11  256687   5
   10 | 0  0   1  0    1  1     1  0      11    1     749   1
   11 | 0  0  85  0  837  8  1195  0  256687  749       1  85
   12 | 0  0   1  0    1  0     1  0       5    1      85   1
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A300630, A306231, A359806, A359888 (denominators).

Programs

PARI

See Links section.

Formula

A(n, k) = A(k, n).

A(n, n) = 1.

A(n, 2*n) = 0 iff n belongs to A300630.

A(A306231(n), A306231(n+1)) = 0.

A(n, A359806(n)) = 0.