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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.
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%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