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.

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

1,2

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*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

Crossrefs

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

Sequence in context: A324331 A101410 A110991 * A352808 A076990 A330434

Adjacent sequences: A262939 A262940 A262941 * A262943 A262944 A262945

Keyword

nonn

Author

Max Barrentine, Oct 05 2015

Extensions

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

Status

approved