A257337 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "4" arm.

4, 9, 13, 23, 16, 35, 24, 41, 30, 47, 40, 53, 42, 55, 54, 71, 60, 77, 72, 85, 82, 93, 88, 101, 96, 109, 102, 121, 116, 125, 122, 129, 130, 141, 136, 147, 146, 157, 154, 167, 160, 179, 166, 177, 172, 185, 184, 201, 190, 207, 200, 213, 206, 221, 214, 225, 224

Offset

1,1

Comments

Place numbers 2,3,4,5 clockwise around a grid point (see illustration in "Spiral" link). 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 4 arm, then the 5 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 four (N,S,E,W) neighbors. Every term in the entire grid must be different.

The four arms are A257335, A257336, A257337, A257338.

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, Spiral showing initial terms of A257335-A257338

Crossrefs

Cf. A064413, A257321-A257340.

Sequence in context: A042125 A041905 A098004 * A056227 A048261 A340771

Adjacent sequences: A257334 A257335 A257336 * A257338 A257339 A257340

Keyword

nonn

Author

N. J. A. Sloane, Apr 21 2015

Extensions

Corrected a(4)-a(9) and more terms from Lars Blomberg, Apr 28 2015

Status

approved