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

0,4

Comments

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

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))

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.

Example

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,

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A330463 A142886 A374019 * A341410 A205341 A195664

Adjacent sequences: A099023 A099024 A099025 * A099027 A099028 A099029

Keyword

nonn,tabl,base,changed

Author

Ralf Stephan, Sep 26 2004

Status

approved