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Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.
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%I #9 Apr 27 2015 10:44:58

%S 3,2,7,9,5,13,15,17,11,4,19,23,21,25,8,29,10,31,14,37,16,41,22,43,47,

%T 27,53,55,26,35,33,49,59,61,67,71,65,73,77,79,83,39,89,97,101,32,103,

%U 20,91,34,107,40,109,38,51,113,57,28,85,44,119,46,81,121,45

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

%C Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.

%C 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.

%C Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Inside an arm, the terms must be distinct.

%C Repetitions between arms are permitted.

%C The four arms are A257325, A257326, A257327, A257328.

%H Lars Blomberg, <a href="/A257326/b257326.txt">Table of n, a(n) for n = 1..10000</a>

%H Popular Computing (Calabasas, CA), <a href="/A257321/a257321.png">Problem 146: Gcd</a>, Vol. 4 (No. 45, Dec 1976), page PC45-4.

%H N. J. A. Sloane, <a href="/A257321/a257321_1.png">Spirals showing initial terms of A257321-A257332</a>

%Y Cf. A064413, A257321-A257340.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 21 2015

%E More terms from _Lars Blomberg_, Apr 27 2015