Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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