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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A009785

Adjacent sequences:  A309814 A309815 A309816 * A309818 A309819 A309820

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Aug 18 2019

STATUS

approved

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Last modified January 21 22:03 EST 2021. Contains 340352 sequences. (Running on oeis4.)