A370049 Square array A(n, k), n, k >= 0, read by antidiagonals; for any n and k >= 0 with respective binary expansions Sum_{i > 0} b_i*2^(i-1) and Sum_{i > 0} c_i*2^(i-1), the binary expansion of A(n, k) is Sum_{i > 0} d_i*2^(i-1) with d_i = (Sum_{k divides i} b_k*c_{i/k}) mod 2 for any i > 0.
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 8, 3, 0, 0, 4, 10, 10, 4, 0, 0, 5, 32, 9, 32, 5, 0, 0, 6, 34, 36, 36, 34, 6, 0, 0, 7, 40, 39, 256, 39, 40, 7, 0, 0, 8, 42, 46, 260, 260, 46, 42, 8, 0, 0, 9, 128, 45, 288, 257, 288, 45, 128, 9, 0, 0, 10, 130, 136, 292, 294, 294, 292, 136, 130, 10, 0
Offset: 0
Examples
Array A(n, k) begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10
----+-------------------------------------------------------------
0 | 0 0 0 0 0 0 0 0 0 0 0
1 | 0 1 2 3 4 5 6 7 8 9 10
2 | 0 2 8 10 32 34 40 42 128 130 136
3 | 0 3 10 9 36 39 46 45 136 139 130
4 | 0 4 32 36 256 260 288 292 2048 2052 2080
5 | 0 5 34 39 260 257 294 291 2056 2061 2090
6 | 0 6 40 46 288 294 264 270 2176 2182 2216
7 | 0 7 42 45 292 291 270 265 2184 2191 2210
8 | 0 8 128 136 2048 2056 2176 2184 32768 32776 32896
9 | 0 9 130 139 2052 2061 2182 2191 32776 32769 32906
10 | 0 10 136 130 2080 2090 2216 2210 32896 32906 32776
Programs
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PARI
bits(n) = { my (b=vector(hammingweight(n))); for (k=1, #b, n-=2^b[k]=valuation(n,2)); return (b); } A(n, k) = { my (bn = bits(2*n), bk = bits(2*k), v = 0, e); for (i = 1, #bn, for (j = 1, #bk, e = bn[i] * bk[j] - 1; v = bitxor(v, 2^e););); return (v); }
Comments