A309817 - OEIS

%I #10 Aug 23 2019 13:44:50

%S 1,12,45,50,80,144,162,294,448,847,1690,1728,1875,1944,2025,2500,2816,

%T 3179,3872,4000,4312,4693,6615,7290,7406,8228,9600,11907,12544,13312,

%U 15979,18900,20280,22103,23328,24010,28314,32256,33524,37856,37975,39600,45177

%N 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).

%C 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:

%C - 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),

%C - 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.

%C 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.

%C This sequence is a generalization of A275897 and of A309362 to a space with infinite dimensions.

%H Rémy Sigrist, <a href="/A309817/a309817.gp.txt">PARI program for A309817</a>

%e We first visit the origin and place our first queen on it.

%e Hence a(1) = Product_{k>=0} prime(k+1)^0 = 1.

%e This first queen attacks every point X such that f(X) is in A072774.

%e The second queen is placed at position (2, 1, 0, 0, 0...}; a(2) = 2^2 * 3 = 12.

%o (PARI) See Links section.

%Y Cf. A072774, A275897, A309362.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Aug 18 2019