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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..43.

Rémy Sigrist, PARI program for A309817

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A072774, A275897, A309362.

Sequence in context: A100156 A320998 A294521 * A340305 A194284 A355446

Adjacent sequences: A309814 A309815 A309816 * A309818 A309819 A309820

Keyword

nonn

Author

Rémy Sigrist, Aug 18 2019

Status

approved