A026480 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.

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, 57, 59, 61, 67, 69, 71, 73, 79, 83, 87, 89, 93, 97, 101, 103, 107, 109, 111, 113, 123, 127, 128, 129, 131, 137, 139, 141, 149, 151, 157, 159, 160, 163, 167, 173, 177, 179, 181

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

From David A. Corneth, Sep 24 2016 (Start):

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]}.

(End)

Links

• David A. Corneth, Table of n, a(n) for n = 1..23405 (all terms up to 10^5).
• David A. Corneth, PARI program

Crossrefs

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.

Programs

Mathematica

a = {1, 2, 4}; no = {1 2 4};
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 *)

Extensions

Name corrected by Charles R Greathouse IV, Sep 23 2016