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%I #16 Aug 17 2017 22:27:52
%S 1,2,4,5,8,9,11,12,16,18,19,21,26,28,29,32,33,35,36,39,43,44,46,47,54,
%T 56,59,60,62,63,68,69,71,72,80,82,86,88,91,93,94,99,103,106,113,115,
%U 116,120,122,127,130,131,133,134,137,141,142,144,145,149,154
%N Smallest increasing natural number sequence without any length 3 equidistant arithmetic subsequences.
%C If the restriction "increasing" is removed sequence A094870 is obtained.
%H Nathaniel Johnston, <a href="/A101884/b101884.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="http://oeis.org/wiki/Index_to_OEIS:_Section_No#non_averaging">Index entries related to non-averaging sequences</a>
%e 3 is out because of 1,2,3. 7 is out because of 1,4,7.
%e 8 is allowed even though 2,5,8 appears in the sequence, because 2, 5, and 8 are not spaced equidistant within the sequence.
%p lim:=61: a[1]:=1:a[2]:=2: for n from 3 to lim do na := {}: for j from 1 to floor((n-1)/2) do na := na union {2*a[n-j]-a[n-2*j]}: od: for j from a[n-1]+1 do if(not member(j,na))then a[n]:=j:break: fi: od:od: seq(a[n],n=1..lim); # _Nathaniel Johnston_, Jun 16 2011
%Y Cf. A101885, A101886, A101888. Also A094870.
%K nonn,easy
%O 1,2
%A Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 20 2004
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