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

1,50

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).

Links

Table of n, a(n) for n=1..91.

Rémy Sigrist, PARI program

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A374248 A300717 A191928 * A033148 A281084 A186230

Adjacent sequences: A359884 A359885 A359886 * A359888 A359889 A359890

Keyword

nonn,base,frac,tabf

Author

Rémy Sigrist, Jan 17 2023

Status

approved