A257338 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "5" arm.

5, 6, 17, 12, 29, 18, 37, 28, 43, 36, 49, 46, 57, 52, 63, 62, 73, 70, 81, 76, 87, 80, 99, 92, 105, 104, 111, 112, 123, 118, 131, 124, 135, 134, 143, 140, 153, 148, 159, 158, 171, 164, 181, 168, 187, 174, 197, 180, 203, 192, 211, 198, 217, 212, 229, 218, 239

Offset: 1

Author

N. J. A. Sloane, Apr 21 2015

Keywords

• nonn

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.

Extensions

Corrected a(3)-a(9) and more terms from Lars Blomberg, Apr 28 2015