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

%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*k-n], 2*V[2*k-n]-V[k],(V[k]+V[2*k-n])/2]),k=ceil((n+1)/2)..n-1)};

%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..n-1); # _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 b-file. - _N. J. A. Sloane_, Nov 26 2015

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Last modified August 5 23:35 EDT 2024. Contains 374957 sequences. (Running on oeis4.)