cp's OEIS Frontend

A274820 Spiral constructed on the nodes of the infinite triangular net in which each term is the least nonnegative integer such that no diagonal contains a repeated term.

%I A274820 #67 Mar 07 2020 13:50:20
%S A274820 0,1,2,1,2,1,2,0,3,0,4,3,5,3,4,5,3,4,6,5,6,7,4,6,5,7,6,3,0,6,5,7,0,6,
%T A274820 7,5,4,8,1,3,6,8,1,9,7,8,2,4,9,8,2,10,11,8,9,10,12,3,8,9,7,10,9,2,4,8,
%U A274820 5,10,2,11,9,11,0,10,7,8,6,0,9,7,10,12,7,1,4,8,5,11,1,10,12,9,5,11,10,13,12,11,13,14
%N A274820 Spiral constructed on the nodes of the infinite triangular net in which each term is the least nonnegative integer such that no diagonal contains a repeated term.
%C A274820 Also spiral constructed on the infinite hexagonal grid in which each term is the least nonnegative integer such that no diagonal of successive adjacent cells contains a repeated term. Every number is located in the center of a hexagonal cell. Every cell is also the center of three diagonals of successive adjacent cells.
%C A274820 Presumably every line of cells with slope a multiple of 60 degrees (not necessarily passing through the central cell) is a permutation of the nonnegative numbers. See A296343-A296348 for the spokes through the central cell. - _N. J. A. Sloane_, Dec 12 2017
%H A274820 Rémy Sigrist, <a href="/A274820/b274820.txt">Table of n, a(n) for n = 0..120400</a>
%H A274820 F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.
%H A274820 Rémy Sigrist, <a href="/A274820/a274820.gp.txt">PARI program for A274820</a>
%H A274820 Rémy Sigrist, <a href="/A274820/a274820_1.png">Colored illustration of the first 200 windings of the spiral</a> (where the color is a function of a(n))
%H A274820 N. J. A. Sloane, <a href="/A274820/a274820.png">Illustration of initial terms drawn as a spiral on the hexagonal grid</a> (the starting cell is marked in black).
%F A274820 a(n) = A274821(n) - 1.
%e A274820 Illustration of initial terms as a spiral:
%e A274820 .
%e A274820 .                   9 - 4 - 2 - 8 - 7
%e A274820 .                  /                 \
%e A274820 .                 8   3 - 6 - 7 - 5   9
%e A274820 .                /   /             \   \
%e A274820 .               2   0   5 - 3 - 4   6   1
%e A274820 .              /   /   /         \   \   \
%e A274820 .            10   6   3   1 - 2   0   4   8
%e A274820 .            /   /   /   /     \   \   \   \
%e A274820 .          11   5   4   2   0 - 1   3   7   6
%e A274820 .            \   \   \   \         /   /   /
%e A274820 .             8   7   5   1 - 2 - 0   6   3
%e A274820 .              \   \   \             /   /
%e A274820 .               9   0   3 - 4 - 6 - 5   1
%e A274820 .                \   \                 /
%e A274820 .                10   6 - 7 - 5 - 4 - 8
%e A274820 .                  \
%e A274820 .                  12 - 3 - 8 - 9 - 7
%e A274820 .
%o A274820 (PARI) See Links section.
%Y A274820 Cf. A001477, A269526, A274528 (square array), A274641 (spiral on the square grid), A274650 (right triangle), A274821, A274920, A274921, A275606, A275610, A296339.
%Y A274820 A296342 says when n first appears.
%Y A274820 See A296343-A296348 for the spokes.
%K A274820 nonn,look
%O A274820 0,3
%A A274820 _Omar E. Pol_, Jul 09 2016