A359888 Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the denominator 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 A359887 for the numerators.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 15, 4, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 63, 1, 5, 1, 63, 1, 1, 1, 1, 1, 1, 15, 15, 1, 1, 1, 1, 1, 1, 63, 1, 455, 6, 455, 1, 63, 1, 1, 1, 1, 15, 1, 8, 63, 63, 8, 1, 15, 1, 1, 1, 1, 1023, 1, 585, 8, 7, 8, 585, 1, 1023, 1, 1

Offset: 1

Author

Rémy Sigrist, Jan 17 2023

Keywords

• nonn
• base
• frac
• tabf

Comments

A359887(n, k)/A(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
  ----+-----------------------------------------------------
    1 | 1  1     1  1      1     1      1  1        1      1
    2 | 1  2     1  1      1     1      1  1        1      1
    3 | 1  1     3  4     15     1     63  1       63     15
    4 | 1  1     4  4      1     1      1  1        1      1
    5 | 1  1    15  1      5    15    455  8      585     15
    6 | 1  1     1  1     15     6     63  8       63     30
    7 | 1  1    63  1    455    63      7  8       63    455
    8 | 1  1     1  1      8     8      8  8        1      1
    9 | 1  1    63  1    585    63     63  1        9    117
   10 | 1  1    15  1     15    30    455  1      117     10
   11 | 1  1  1023  1  11275  1023  76461  1  3243933  11275
   12 | 1  1    12  1     15     1     63  1       63     15
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A300630, A306231, A359806, A359887 (numerators).

Programs

PARI

See Links section.

Formula

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

A(n, n) = n.