cp's OEIS Frontend

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.

%I A262942 #20 Mar 04 2025 07:37:14
%S A262942 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 A262942 31,28,23,32,29,34,37,38,40,41,35,30,42,46,47,54,36,33,45,43,49,39,48,
%U A262942 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 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.
%C A262942 Conjectured permutation of the natural numbers.
%H A262942 Robert Israel, <a href="/A262942/b262942.txt">Table of n, a(n) for n = 1..10000</a>
%e A262942 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 A262942 N:= 1000: # to get all terms before the first > N
%p A262942 V:= Vector(N):
%p A262942 S:= Vector(N):
%p A262942 firstav:= 1;
%p A262942 for n from 1 to N do
%p A262942     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)};
%p A262942     for v from firstav to N do
%p A262942       if S[v] <> 0 and v = firstav then firstav:= v+1 fi;
%p A262942       if S[v] = 0 and not member(v, forbid) then
%p A262942         V[n]:= v;
%p A262942         S[v]:= 1;
%p A262942         break
%p A262942       fi
%p A262942     od;
%p A262942     if v > N then break fi;
%p A262942 od:
%p A262942 seq(V[i],i=1..n-1); # _Robert Israel_, Nov 15 2015
%Y A262942 A229037 has a very similar definition, but a totally different graph.
%K A262942 nonn
%O A262942 1,2
%A A262942 _Max Barrentine_, Oct 05 2015
%E A262942 Added more terms from b-file. - _N. J. A. Sloane_, Nov 26 2015