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A268811 Sequence of positive integers where each is chosen to be as small as possible subject to the condition that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a geometric progression.

%I A268811 #22 May 23 2025 14:30:38
%S A268811 1,1,2,1,1,2,2,3,3,1,1,2,1,1,2,2,3,3,2,3,3,5,5,6,5,5,6,1,1,2,1,1,2,2,
%T A268811 3,3,1,1,2,1,1,2,2,3,3,2,3,3,5,5,6,5,5,6,2,3,3,5,5,6,5,5,6,6,7,7,6,7,
%U A268811 7,8,8,10,6,7,7,6,7,7,8,8,10,1,1,2,1,1,2,2,3,3,1,1,2,1,1,2,2,3,3,2,3,3,5,5,6,5,5,6,1,1,2,1,1,2,2,3,3,1,1,2,1,1,2,2,3,3,2
%N A268811 Sequence of positive integers where each is chosen to be as small as possible subject to the condition that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a geometric progression.
%C A268811 Apparently: all terms belong to A000452, and for any k > 0, the value A000452(k) first appears at index A265316(k+1). - _Rémy Sigrist_, May 13 2021
%H A268811 Rémy Sigrist, <a href="/A268811/b268811.txt">Table of n, a(n) for n = 1..10000</a>
%H A268811 Rémy Sigrist, <a href="/A268811/a268811.txt">C program for A268811</a>
%o A268811 (Python)
%o A268811 A268811_list = []
%o A268811 for n in range(1000):
%o A268811     i, j, b = 1, 1, set()
%o A268811     while n-2*i >= 0:
%o A268811         b.add(A268811_list[n-i]**2/A268811_list[n-2*i])
%o A268811         i += 1
%o A268811         while j in b:
%o A268811             b.remove(j)
%o A268811             j += 1
%o A268811     A268811_list.append(j)
%o A268811 (C) // See Links section.
%Y A268811 Cf. A000452, A229037, A265316.
%K A268811 nonn,easy
%O A268811 1,3
%A A268811 _Aaron David Fairbanks_, Feb 13 2016