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

1,1

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

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).

Sequence in context: A082000 A100434 A096876 * A115388 A187995 A296277

Adjacent sequences: A257327 A257328 A257329 * A257331 A257332 A257333

Keyword

nonn

Author

N. J. A. Sloane, Apr 21 2015

Extensions

More terms from Lars Blomberg, Apr 27 2015

Status

approved