A377930 Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) = max(A007814(n), A007814(k)).

0, 1, 1, 0, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 0, 1, 1, 2, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 3, 1, 1, 2, 2, 1, 1, 3, 0, 3, 0, 2, 0, 2, 0, 3, 0, 1, 1, 3, 2, 1, 1, 2, 3, 1, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 2, 1, 1, 2, 3, 1, 1, 3, 2, 1, 1, 2, 0, 2, 0, 2, 0, 3, 0, 3, 0, 2, 0, 2, 0

Offset: 1

Author

Rémy Sigrist, Nov 11 2024

Keywords

• nonn
• easy
• tabl

Comments

Let K_0 = [0], and for any m > 0, K_m is obtained by arranging four copies of K_{m-1} around a "plus" shape made of m's as follows:

+---------+---+---------+

| | m | |

| | | |

| K_{m-1} | . | K_{m-1} |

| | . | |

| | . | |

+---+ +---------+ +---------+

K_0 = | 0 |, for m > 0, K_m = |m ... m ... m|

+---+ +---------+ +---------+

| | . | |

| | . | |

| K_{m-1} | . | K_{m-1} |

| | | |

| | m | |

+---------+---+---------+

The square array A is the limit of K_m as m tends to infinity.

Examples

			Array A(n, k) begins:
    +---+---+---+---+---+---+---+
    | 0 | 1 | 0 | 2 | 0 | 1 | 0 |
    +---+   +---+   +---+   +---+
    | 1   1   1 | 2 | 1   1   1 |
    +---+   +---+   +---+   +---+
    | 0 | 1 | 0 | 2 | 0 | 1 | 0 |
    +---+---+---+   +---+---+---+
    | 2   2   2   2   2   2   2 |
    +---+---+---+   +---+---+---+
    | 0 | 1 | 0 | 2 | 0 | 1 | 0 |
    +---+   +---+   +---+   +---+
    | 1   1   1 | 2 | 1   1   1 |
    +---+   +---+   +---+   +---+
    | 0 | 1 | 0 | 2 | 0 | 1 | 0 |
    +---+---+---+---+---+---+---+
		

Crossrefs

Cf. A003984, A007814, A053398.

Programs

Mathematica

A[n_,k_]:=Max[IntegerExponent[n,2],IntegerExponent[k,2]]; Table[A[n-k+1,k],{n,13},{k,n}]//Flatten (* Stefano Spezia, Nov 13 2024 *)

PARI

A(n, k) = max(valuation(n, 2), valuation(k, 2))

Formula

A(n, k) = A(k, n).

A(n, 0) = A(n, n) = A007814(n).