%I #17 Nov 28 2015 18:03:18
%S 1,2,4,5,8,3,7,6,10,11,14,9,16,12,13,19,15,18,20,21,26,17,22,24,25,27,
%T 31,28,23,32,29,34,37,38,40,41,35,30,42,46,47,54,36,33,45,43,49,39,48,
%U 50,55,52,53,44,59,57,51,60,56,61,62,67,58,69,64,72,66,68,76,71,73,77,65,75,63,88,89,80,78,74,83,79,70,90,94,82,81,84,85,91,87,101
%N Sequence of positive integers where each is chosen to be as small as possible subject to the conditions that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression (in any order) and that no term repeats.
%C Conjectured permutation of the natural numbers.
%H Robert Israel, <a href="/A262942/b262942.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 4, 3 is not available because (a(2)=2, 3, a(3)=4} form an arithmetic progression, 1,2,4 are already used, so a(4) = 5.  _Robert Israel_, Nov 15 2015
%p N:= 1000: # to get all terms before the first > N
%p V:= Vector(N):
%p S:= Vector(N):
%p firstav:= 1;
%p for n from 1 to N do
%p forbid:= {seq(op([2*V[k]V[2*kn], 2*V[2*kn]V[k],(V[k]+V[2*kn])/2]),k=ceil((n+1)/2)..n1)};
%p for v from firstav to N do
%p if S[v] <> 0 and v = firstav then firstav:= v+1 fi;
%p if S[v] = 0 and not member(v, forbid) then
%p V[n]:= v;
%p S[v]:= 1;
%p break
%p fi
%p od;
%p if v > N then break fi;
%p od:
%p seq(V[i],i=1..n1); # _Robert Israel_, Nov 15 2015
%Y A229037 has a very similar definition, but a totally different graph.
%K nonn
%O 1,2
%A _Max Barrentine_, Oct 05 2015
%E Added more terms from bfile.  _N. J. A. Sloane_, Nov 26 2015
