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A359887
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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.
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2
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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
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OFFSET
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1,50
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COMMENTS
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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).
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LINKS
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FORMULA
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A(n, k) = A(k, n).
A(n, n) = 1.
A(n, 2*n) = 0 iff n belongs to A300630.
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EXAMPLE
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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
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,base,frac,tabf
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AUTHOR
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STATUS
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approved
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