A262942 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+2*k) (for any j and k) form an arithmetic progression (in any order) and that no term repeats.

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, 31, 28, 23, 32, 29, 34, 37, 38, 40, 41, 35, 30, 42, 46, 47, 54, 36, 33, 45, 43, 49, 39, 48, 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

Offset: 1

Author

Max Barrentine, Oct 05 2015

Keywords

• nonn

Comments

Conjectured permutation of the natural numbers.

Examples

			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
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A229037 has a very similar definition, but a totally different graph.

Programs

Maple

N:= 1000: # to get all terms before the first > N
V:= Vector(N):
S:= Vector(N):
firstav:= 1;
for n from 1 to N do
    forbid:= {seq(op([2*V[k]-V[2*k-n], 2*V[2*k-n]-V[k],(V[k]+V[2*k-n])/2]),k=ceil((n+1)/2)..n-1)};
    for v from firstav to N do
      if S[v] <> 0 and v = firstav then firstav:= v+1 fi;
      if S[v] = 0 and not member(v, forbid) then
        V[n]:= v;
        S[v]:= 1;
        break
      fi
    od;
    if v > N then break fi;
od:
seq(V[i],i=1..n-1); # Robert Israel, Nov 15 2015

Extensions

Added more terms from b-file. - N. J. A. Sloane, Nov 26 2015