A257329 - OEIS

%I #13 Apr 30 2015 20:03:41

%S 2,11,13,25,21,37,27,10,39,20,71,24,85,32,95,107,115,121,125,46,145,

%T 151,155,99,167,105,181,117,197,205,211,141,223,147,76,159,86,263,72,

%U 259,135,289,30,311,60,301,94,337,116,341,343,110,359,112,237,122,389

%N Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" 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. Every term in the entire grid must be different.

%C The four arms are A257329, A257330, A257331, A257332.

%C Conjecture: every number > 1 appears in one of the four arms.

%H Lars Blomberg, <a href="/A257329/b257329.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, A257347 (the union list).

%K nonn

%O 1,1

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

%E More terms from _Lars Blomberg_, Apr 27 2015