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A274821
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.
12
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, 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, 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
OFFSET
0,2
COMMENTS
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.
FORMULA
a(n) = A274820(n) + 1.
EXAMPLE
Illustration of initial terms as a spiral:
.
. 10 - 5 - 3 - 9 - 8
. / \
. 9 4 - 7 - 8 - 6 10
. / / \ \
. 3 1 6 - 4 - 5 7 2
. / / / \ \ \
. 11 7 4 2 - 3 1 5 9
. / / / / \ \ \ \
. 12 6 5 3 1 - 2 4 8 7
. \ \ \ \ / / /
. 9 8 6 2 - 3 - 1 7 4
. \ \ \ / /
. 10 1 4 - 5 - 7 - 6 2
. \ \ /
. 11 7 - 8 - 6 - 5 - 9
. \
. 13 - 4 - 9 - 10 - 8
.
CROSSREFS
Cf. A269526 (square array), A274640 (square spiral), A274651 (right triangle), A274820, A274920, A274921, A275606, A275610.
Sequence in context: A339601 A117666 A274921 * A275720 A307200 A339092
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 09 2016
STATUS
approved