%I #8 Jan 19 2023 11:10:12
%S 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,
%T 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,
%U 0,1,0,1,8,8,1,0,1,0,0,0,0,85,0,37,1,1,1,37,0,85,0,0
%N 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.
%C 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).
%H Rémy Sigrist, <a href="/A359887/a359887.gp.txt">PARI program</a>
%F A(n, k) = A(k, n).
%F A(n, n) = 1.
%F A(n, 2*n) = 0 iff n belongs to A300630.
%F A(A306231(n), A306231(n+1)) = 0.
%F A(n, A359806(n)) = 0.
%e Square array A(n, k) begins:
%e n\k | 1 2 3 4 5 6 7 8 9 10 11 12
%e ----+------------------------------------------------------
%e 1 | 1 0 0 0 0 0 0 0 0 0 0 0
%e 2 | 0 1 0 0 0 0 0 0 0 0 0 0
%e 3 | 0 0 1 1 1 0 1 0 5 1 85 1
%e 4 | 0 0 1 1 0 0 0 0 0 0 0 0
%e 5 | 0 0 1 0 1 2 57 1 37 1 837 1
%e 6 | 0 0 0 0 2 1 8 1 2 1 8 0
%e 7 | 0 0 1 0 57 8 1 1 1 1 1195 1
%e 8 | 0 0 0 0 1 1 1 1 0 0 0 0
%e 9 | 0 0 5 0 37 2 1 0 1 11 256687 5
%e 10 | 0 0 1 0 1 1 1 0 11 1 749 1
%e 11 | 0 0 85 0 837 8 1195 0 256687 749 1 85
%e 12 | 0 0 1 0 1 0 1 0 5 1 85 1
%o (PARI) See Links section.
%Y Cf. A300630, A306231, A359806, A359888 (denominators).
%K nonn,base,frac,tabf
%O 1,50
%A _Rémy Sigrist_, Jan 17 2023
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