%I #17 May 14 2021 02:58:51
%S 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 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 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 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 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 Rémy Sigrist, <a href="/A268811/b268811.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A268811/a268811.txt">C program for A268811</a>
%o (Python)
%o A268811_list = []
%o for n in range(1000):
%o ....i, j, b = 1, 1, set()
%o ....while n-2*i >= 0:
%o ........b.add(A268811_list[n-i]**2/A268811_list[n-2*i])
%o ........i += 1
%o ........while j in b:
%o ............b.remove(j)
%o ............j += 1
%o ....A268811_list.append(j)
%o (C) See Links section.
%Y Cf. A000452, A229037, A265316.
%K nonn,easy
%O 1,3
%A _Aaron David Fairbanks_, Feb 13 2016