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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.
2
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).
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
KEYWORD
nonn,base,frac,tabf
AUTHOR
Rémy Sigrist, Jan 17 2023
STATUS
approved