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

1,5

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).

Links

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

Rémy Sigrist, PARI program

Formula

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

A(n, n) = n.

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A294333 A321125 A205617 * A204112 A186027 A359250

Adjacent sequences: A359885 A359886 A359887 * A359889 A359890 A359891

Keyword

nonn,base,frac,tabf

Author

Rémy Sigrist, Jan 17 2023

Status

approved