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%I #42 Sep 13 2020 01:59:12
%S 1,2,3,2,3,2,3,1,4,1,5,4,6,4,5,6,4,5,7,6,7,8,5,7,6,8,7,4,1,7,6,8,1,7,
%T 8,6,5,9,2,4,7,9,2,10,8,9,3,5,10,9,3,11,12,9,10,11,13,4,9,10,8,11,10,
%U 3,5,9,6,11,3,12,10,12,1,11,8,9,7,1,10,8,11,13,8,2,5,9,6,12,2,11,13,10,6,12,11,14,13,12,14,15
%N Hexagonal spiral constructed on the nodes of the infinite triangular net in which each term is the least positive integer such that no diagonal contains a repeated term.
%C Also spiral constructed on the infinite hexagonal grid in which each term is the least positive 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.
%F a(n) = A274820(n) + 1.
%e Illustration of initial terms as a spiral:
%e .
%e . 10 - 5 - 3 - 9 - 8
%e . / \
%e . 9 4 - 7 - 8 - 6 10
%e . / / \ \
%e . 3 1 6 - 4 - 5 7 2
%e . / / / \ \ \
%e . 11 7 4 2 - 3 1 5 9
%e . / / / / \ \ \ \
%e . 12 6 5 3 1 - 2 4 8 7
%e . \ \ \ \ / / /
%e . 9 8 6 2 - 3 - 1 7 4
%e . \ \ \ / /
%e . 10 1 4 - 5 - 7 - 6 2
%e . \ \ /
%e . 11 7 - 8 - 6 - 5 - 9
%e . \
%e . 13 - 4 - 9 - 10 - 8
%e .
%Y Cf. A269526 (square array), A274640 (square spiral), A274651 (right triangle), A274820, A274920, A274921, A275606, A275610.
%K nonn
%O 0,2
%A _Omar E. Pol_, Jul 09 2016
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