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A257329
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Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.
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5
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2, 11, 13, 25, 21, 37, 27, 10, 39, 20, 71, 24, 85, 32, 95, 107, 115, 121, 125, 46, 145, 151, 155, 99, 167, 105, 181, 117, 197, 205, 211, 141, 223, 147, 76, 159, 86, 263, 72, 259, 135, 289, 30, 311, 60, 301, 94, 337, 116, 341, 343, 110, 359, 112, 237, 122, 389
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OFFSET
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1,1
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COMMENTS
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Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Every term in the entire grid must be different.
Conjecture: every number > 1 appears in one of the four arms.
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LINKS
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Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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