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%I #11 May 26 2019 14:21:36
%S 1,3,4,5,6,7,8,9,10,11,13,14,16,17,19,22,23,25,26,29,31,34,37,38,41,
%T 43,46,47,49,53,58,59,61,62,67,71,73,74,79,81,82,83,86,89,94,97,101,
%U 103,106,107,109,113,118,121,122,127,131,134,137,139,142,146,149,151,157
%N a(n) = least positive integer > a(n-1) and not a(i)*a(j)*a(k) for 1<=i<j<k<n.
%t a = {1, 3, 4}; no = {1 3 4};
%t Do[x = SelectFirst[Range[Last[a] + 1, 1000], ! MemberQ[no, #] &]; AppendTo[a, x]; no = Union[Times @@@ Subsets[a, {3}]], 62]; 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,easy
%O 1,2
%A _Clark Kimberling_
%E More terms from Todd Will (towill(AT)davidson.edu).
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