

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



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
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OFFSET

1,2


COMMENTS

Conjectured permutation of the natural numbers.


LINKS

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


EXAMPLE

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


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*kn], 2*V[2*kn]V[k], (V[k]+V[2*kn])/2]), k=ceil((n+1)/2)..n1)};
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..n1); # Robert Israel, Nov 15 2015


CROSSREFS

A229037 has a very similar definition, but a totally different graph.
Sequence in context: A324331 A101410 A110991 * A076990 A330434 A330424
Adjacent sequences: A262939 A262940 A262941 * A262943 A262944 A262945


KEYWORD

nonn


AUTHOR

Max Barrentine, Oct 05 2015


EXTENSIONS

Added more terms from bfile.  N. J. A. Sloane, Nov 26 2015


STATUS

approved



