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A224853 Lexicographically earliest sequence of nonnegative integers which does not contain a three-term arithmetic, geometric, or harmonic subsequence.

%I A224853 #39 Feb 26 2024 19:17:47
%S A224853 0,1,3,4,10,11,13,14,29,30,32,33,38,39,41,42,85,86,88,89,94,95,97,98,
%T A224853 112,113,115,116,122,123,125,238,248,251,252,255,257,260,261,273,275,
%U A224853 278,279,287,288,292,330,331,334,335
%N A224853 Lexicographically earliest sequence of nonnegative integers which does not contain a three-term arithmetic, geometric, or harmonic subsequence.
%C A224853 This sequence diverges from A225571 at 477th term. Here a(477) = 17408, while A225571(477) = 17380. - _Giovanni Resta_, Jul 29 2013
%H A224853 Giovanni Resta, <a href="/A224853/b224853.txt">Table of n, a(n) for n = 1..10000</a>
%e A224853 After terms 0, 1, 3, 4 have been added, the terms 5,...,9 are forbidden by subsequences (3,4,5), (0,3,6), (1,4,7), (0,4,8) and (1,3,9) so the next term is 10.
%o A224853 (Python)
%o A224853 # Program that generates all values of a(x) less than a given input n.
%o A224853 def a(n):
%o A224853       seq=[0, 1]
%o A224853       for x in range(2, n+1):
%o A224853           c=0
%o A224853           for y in seq:
%o A224853               if (x+y)/2 not in seq:
%o A224853                   if (x*y)**0.5 not in seq[1:]:
%o A224853                       if (2*x*y)/(x+y) not in seq[1:]:
%o A224853                           c+=1
%o A224853           if c==len(seq):
%o A224853               seq.append(x)
%o A224853       return seq
%Y A224853 Cf. A225571, A003278, A005836, A000452.
%K A224853 nonn,look
%O A224853 1,3
%A A224853 _Timur Vural_, Jul 28 2013