A099026 Array x AND NOT y, read by rising antidiagonals.

0, 1, 0, 2, 0, 0, 3, 2, 1, 0, 4, 2, 0, 0, 0, 5, 4, 1, 0, 1, 0, 6, 4, 4, 0, 2, 0, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 6, 4, 4, 0, 2, 0, 0, 0, 9, 8, 5, 4, 1, 0, 1, 0, 1, 0, 10, 8, 8, 4, 2, 0, 0, 0, 2, 0, 0, 11, 10, 9, 8, 3, 2, 1, 0, 3, 2, 1, 0, 12, 10, 8, 8, 8, 2, 0, 0, 4, 2, 0, 0, 0, 13, 12, 9, 8, 9, 8, 1

Offset: 0

Author

Ralf Stephan, Sep 26 2004

Keywords

• nonn
• tabl
• base

Comments

For n>0, the n-th row and the differences of the n-th column have period 2^floor(log_(n)+1).

Examples

			0,0,0,0,0,0,
1,0,1,0,1,0,
2,2,0,0,2,2,
3,2,1,0,3,2,
4,4,4,4,0,0,
5,4,5,4,1,0,
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010
• Rémy Sigrist, Colored representation of the table for n, k < 2^10 (the color at (x, y) is function of T(x, y))

Crossrefs

Rows include A000004, A059841. Columns include A001477, A052928. Antidiagonal sums are in A099027.

Cf. A003985 (AND), A003986 (OR), A003987 (XOR).

Programs

Mathematica

Table[BitAnd[x - y, BitNot[y]], {x, 0, 15}, {y, 0, x}] (* Paolo Xausa, Sep 30 2024 *)

PARI

T(x,y)=bitnegimply(x,y)

Formula

T(x, y) = x AND NOT y. The AND NOT operation satisfies the bitwise truth table: (0, 0) = 0, (0, 1) = 0, (1, 0) = 1, (1, 1) = 0.