A224853 - OEIS

%I #39 Feb 26 2024 19:17:47

%S 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 112,113,115,116,122,123,125,238,248,251,252,255,257,260,261,273,275,

%U 278,279,287,288,292,330,331,334,335

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

%C This sequence diverges from A225571 at 477th term. Here a(477) = 17408, while A225571(477) = 17380. - _Giovanni Resta_, Jul 29 2013

%H Giovanni Resta, <a href="/A224853/b224853.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (Python)

%o # Program that generates all values of a(x) less than a given input n.

%o def a(n):

%o       seq=[0, 1]

%o       for x in range(2, n+1):

%o           c=0

%o           for y in seq:

%o               if (x+y)/2 not in seq:

%o                   if (x*y)**0.5 not in seq[1:]:

%o                       if (2*x*y)/(x+y) not in seq[1:]:

%o                           c+=1

%o           if c==len(seq):

%o               seq.append(x)

%o       return seq

%Y Cf. A225571, A003278, A005836, A000452.

%K nonn,look

%O 1,3

%A _Timur Vural_, Jul 28 2013