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A257331
Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "5" arm.
5
5, 6, 19, 8, 35, 43, 16, 53, 67, 45, 79, 55, 89, 91, 69, 113, 36, 131, 63, 139, 75, 44, 111, 50, 173, 52, 185, 58, 123, 68, 215, 74, 229, 235, 241, 251, 253, 265, 277, 275, 287, 80, 307, 295, 317, 165, 331, 213, 323, 78, 349, 195, 367, 225, 371, 365, 397, 249
OFFSET
1,1
COMMENTS
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.
The four arms are A257329, A257330, A257331, A257332.
Conjecture: every number > 1 appears in one of the four arms.
LINKS
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
CROSSREFS
Cf. A064413, A257321-A257340, A257347 (the union list).
Sequence in context: A295972 A333405 A063445 * A240400 A031448 A290254
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 21 2015
EXTENSIONS
More terms from Lars Blomberg, Apr 27 2015
STATUS
approved