cp's OEIS Frontend

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.

%I A359888 #6 Jan 19 2023 11:10:17
%S A359888 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,
%T A359888 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,
%U A359888 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
%N 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.
%C A359888 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).
%H A359888 Rémy Sigrist, <a href="/A359888/a359888.gp.txt">PARI program</a>
%F A359888 A(n, k) = A(k, n).
%F A359888 A(n, n) = n.
%e A359888 Square array A(n, k) begins:
%e A359888   n\k | 1  2     3  4      5     6      7  8        9     10
%e A359888   ----+-----------------------------------------------------
%e A359888     1 | 1  1     1  1      1     1      1  1        1      1
%e A359888     2 | 1  2     1  1      1     1      1  1        1      1
%e A359888     3 | 1  1     3  4     15     1     63  1       63     15
%e A359888     4 | 1  1     4  4      1     1      1  1        1      1
%e A359888     5 | 1  1    15  1      5    15    455  8      585     15
%e A359888     6 | 1  1     1  1     15     6     63  8       63     30
%e A359888     7 | 1  1    63  1    455    63      7  8       63    455
%e A359888     8 | 1  1     1  1      8     8      8  8        1      1
%e A359888     9 | 1  1    63  1    585    63     63  1        9    117
%e A359888    10 | 1  1    15  1     15    30    455  1      117     10
%e A359888    11 | 1  1  1023  1  11275  1023  76461  1  3243933  11275
%e A359888    12 | 1  1    12  1     15     1     63  1       63     15
%o A359888 (PARI) See Links section.
%Y A359888 Cf. A300630, A306231, A359806, A359887 (numerators).
%K A359888 nonn,base,frac,tabf
%O A359888 1,5
%A A359888 _Rémy Sigrist_, Jan 17 2023