A369312 Square array A(n, k), n >= 0, k > 0, read by upwards antidiagonals: P(A(n, k)) is the quotient of the polynomial long division of P(n) by P(k) (where P(m) denotes the polynomial over GF(2) whose coefficients are encoded in the binary expansion of the nonnegative integer m).
0, 1, 0, 2, 0, 0, 3, 1, 0, 0, 4, 1, 1, 0, 0, 5, 2, 1, 0, 0, 0, 6, 2, 3, 0, 0, 0, 0, 7, 3, 3, 1, 0, 0, 0, 0, 8, 3, 2, 1, 1, 0, 0, 0, 0, 9, 4, 2, 1, 1, 1, 0, 0, 0, 0, 10, 4, 7, 1, 1, 1, 1, 0, 0, 0, 0, 11, 5, 7, 2, 1, 1, 1, 0, 0, 0, 0, 0, 12, 5, 6, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0
Offset: 0
Examples
Array A(n, k) begins:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12
----+---------------------------------------
0 | 0 0 0 0 0 0 0 0 0 0 0 0
1 | 1 0 0 0 0 0 0 0 0 0 0 0
2 | 2 1 1 0 0 0 0 0 0 0 0 0
3 | 3 1 1 0 0 0 0 0 0 0 0 0
4 | 4 2 3 1 1 1 1 0 0 0 0 0
5 | 5 2 3 1 1 1 1 0 0 0 0 0
6 | 6 3 2 1 1 1 1 0 0 0 0 0
7 | 7 3 2 1 1 1 1 0 0 0 0 0
8 | 8 4 7 2 2 3 3 1 1 1 1 1
9 | 9 4 7 2 2 3 3 1 1 1 1 1
10 | 10 5 6 2 2 3 3 1 1 1 1 1
11 | 11 5 6 2 2 3 3 1 1 1 1 1
12 | 12 6 4 3 3 2 2 1 1 1 1 1
Programs
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PARI
A(n, k) = { fromdigits(lift(Vec( (Mod(1, 2) * Pol(binary(n))) \ (Mod(1, 2) * Pol(binary(k))))), 2) }
Comments