A309362 -id:A309362 - cp's OEIS frontend

A309817 a(n) is the index of the n-th nonattacking queen placed by a greedy algorithm on a subset of N^N (see Comments for details).

1, 12, 45, 50, 80, 144, 162, 294, 448, 847, 1690, 1728, 1875, 1944, 2025, 2500, 2816, 3179, 3872, 4000, 4312, 4693, 6615, 7290, 7406, 8228, 9600, 11907, 12544, 13312, 15979, 18900, 20280, 22103, 23328, 24010, 28314, 32256, 33524, 37856, 37975, 39600, 45177

Offset: 1

Rémy Sigrist, Aug 18 2019

nonn

We consider an infinite chessboard on the subset S of points X = (x_k){k>=0} of N^N such that Sum{k>=0} x_k is finite:
- any point X = (x_k){k>=0} of S is uniquely identified by the positive number f(X) = Product{k>=0} prime(k+1)^x_k (where prime(k) denotes the k-th prime number),
- two distinct points X = (x_k){k>=0} and Y = (y_k){k>=0} are aligned iff { x_k - y_k, k >= 0 } = { 0, m } for some m > 0.
We traverse S by increasing value of f, and place nonattacking queens as soon as possible; a(n) is the value of f applied to the position of the n-th queen.
This sequence is a generalization of A275897 and of A309362 to a space with infinite dimensions.

			We first visit the origin and place our first queen on it.
Hence a(1) = Product_{k>=0} prime(k+1)^0 = 1.
This first queen attacks every point X such that f(X) is in A072774.
The second queen is placed at position (2, 1, 0, 0, 0...); a(2) = 2^2 * 3 = 12.

Rémy Sigrist, PARI program for A309817

Cf. A072774, A275897, A309362.

PARI
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A309817 a(n) is the index of the n-th nonattacking queen placed by a greedy algorithm on a subset of N^N (see Comments for details).

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