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%I #11 Feb 24 2019 02:24:44
%S 0,1,2,5,7,8,9,12,16,28,29,33,35,37,40,42,51,57,58,59,65,76,78,86,92,
%T 117,123,127,130,131,134,138,141,165,166,182,183,186,187,190,201,203,
%U 205,208,211,215,247,257,268,280,317,329,338,350,352,354,360,395
%N The earliest increasing sequence of nonnegative integers such that if a(j) < a(k) are both in the sequence then a(k) + 2*(a(k) - a(j)) is not.
%C Start an arithmetic progression with any two terms from the sequence; the fourth term of that progression is not allowed to be in the sequence.
%H Nathaniel Johnston, <a href="/A191767/b191767.txt">Table of n, a(n) for n = 1..5000</a>
%e Because 0 and 1 are in the sequence, 1 + 2*(1 - 0) = 3 is not in the sequence. Because 5 and 9 are in the sequence, 9 + 2*(9 - 5) = 17 is not in the sequence.
%p A191767 := proc(n) option remember; local a,k,j; if n <= 2 then n-1 ; else for a from procname(n-1)+1 do atru := true; for j from 1 to n-2 do for k from j+1 to n-1 do if 3*procname(k)-2*procname(j) = a then atru := false; break; end if; end do: if not atru then break; end if; end do: if atru then return a; end if; end do: end if; end proc: # _R. J. Mathar_, Jun 30 2011
%Y Cf. A005836.
%K nonn,easy
%O 1,3
%A _Paul Weisenhorn_, Jun 15 2011
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