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%I #34 May 26 2019 14:21:31
%S 1,2,4,5,6,7,9,11,13,15,17,19,21,23,27,29,31,33,37,39,41,43,47,51,53,
%T 57,59,61,67,69,71,73,79,83,87,89,93,97,101,103,107,109,111,113,123,
%U 127,128,129,131,137,139,141,149,151,157,159,160,163,167,173,177,179,181
%N a(1) = 1, a(2) = 2, a(3) = 4, and for n > 3, a(n) is the least positive integer > a(n-1) not of form a(i)*a(j)*a(k) for 1 <= i <= j <= k < n.
%C From _David A. Corneth_, Sep 24 2016 (Start):
%C Let t be a term of this sequence. Let v = (i, j, m) be a vector of three elements where i is A007814(t), j = A007949(t) and m = A001222(t) - i - j. Then possible vectors v for t up to 100000 are {[0, 0, 0], [0, 0, 1], [0, 0, 4], [0, 0, 7], [0, 1, 1], [0, 1, 4], [0, 2, 0], [0, 3, 0], [0, 4, 3], [0, 5, 3], [0, 6, 2], [0, 7, 2], [0, 8, 1], [0, 9, 1], [0, 10, 0], [1, 0, 0], [1, 0, 3], [1, 0, 6], [1, 1, 0], [1, 1, 3], [1, 1, 6], [1, 4, 2], [1, 5, 2], [1, 6, 1], [1, 7, 1], [1, 8, 0], [1, 9, 0], [2, 0, 0], [2, 3, 2], [2, 5, 1], [2, 7, 0], [3, 0, 2], [3, 0, 5], [3, 1, 2], [3, 1, 5], [3, 3, 1], [3, 4, 1], [3, 5, 0], [3, 6, 0], [4, 2, 1], [4, 2, 4], [4, 4, 0], [5, 0, 1], [5, 0, 4], [5, 1, 1], [5, 1, 4], [5, 2, 0], [5, 3, 0], [6, 0, 3], [6, 1, 0], [6, 1, 3], [7, 0, 0], [7, 3, 2], [8, 0, 2], [8, 1, 2], [8, 3, 1], [8, 5, 0], [9, 2, 1], [9, 4, 0], [10, 0, 1], [10, 1, 1], [10, 2, 0], [10, 3, 0], [11, 1, 0], [12, 0, 0]}.
%C (End)
%H David A. Corneth, <a href="/A026480/b026480.txt">Table of n, a(n) for n = 1..23405</a> (all terms up to 10^5).
%H David A. Corneth, <a href="/A026480/a026480_2.gp.txt">PARI program</a>
%t a = {1, 2, 4}; no = {1 2 4};
%t Do[x = SelectFirst[Range[Last[a] + 1, 1000], ! MemberQ[no, #] &]; AppendTo[a, x]; no = Union[Times @@@ Tuples[a, {3}]], 60]; a (* _Robert Price_, May 26 2019 *)
%Y There are six related sequences: A026477: 1 <= i < j < k < n starting 1,2,3; A026478: 1 <= i <= j <= k < n starting 1,2,3; A026479: 1 <= i < j < k < n starting 1,2,4; A026480: 1 <= i <= j <= k < n starting 1,2,4; A026481: 1 <= i < j < k < n starting 1,3,4; A026482: 1 <= i <= j <= k < n starting 1,3,4.
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name corrected by _Charles R Greathouse IV_, Sep 23 2016
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