A257330 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

3, 4, 17, 29, 31, 41, 49, 33, 61, 18, 73, 51, 77, 57, 28, 109, 34, 127, 38, 87, 62, 157, 40, 163, 169, 175, 187, 193, 64, 209, 203, 221, 227, 239, 153, 245, 171, 269, 177, 281, 293, 299, 189, 313, 201, 106, 207, 70, 219, 100, 347, 84, 361, 96, 379, 243, 391

Offset: 1

Author

N. J. A. Sloane, Apr 21 2015

Keywords

• nonn

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

• Lars Blomberg, Table of n, a(n) for n = 1..10000
• Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
• N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Crossrefs

Cf. A064413, A257321-A257340, A257347 (the union list).

Extensions

More terms from Lars Blomberg, Apr 27 2015