A282193 a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings (forward or backward) of length greater than 1.

1, 1, 2, 4, 6, 12, 36, 96, 240, 480, 1440, 5760, 17280, 40320, 120960, 483840, 1935360, 5806080, 17418240, 69672960, 348364800, 1045094400, 3832012800, 15328051200, 76640256000, 229920768000, 919683072000, 4598415360000, 22072393728000, 71735279616000, 286941118464000, 1434705592320000

Offset: 1

Author

Peter Kagey, Feb 08 2017

Keywords

• nonn

Examples

			a(1)  = 1    via [1];
a(2)  = 1    via [1,1];
a(3)  = 2    via [1,1,2];
a(4)  = 4    via [1,1,2,2];
a(5)  = 6    via [1,1,2,3,1];
a(6)  = 12   via [1,1,2,2,3,1];
a(7)  = 36   via [1,1,2,2,3,3,1];
a(8)  = 96   via [1,1,2,2,3,1,4,2];
a(9)  = 240  via [1,1,2,2,3,1,4,5,1];
a(10) = 480  via [1,1,2,2,3,1,4,2,5,1];
a(11) = 1440 via [1,1,2,2,3,3,1,4,2,5,1];
a(12) = 5760 via [1,1,2,2,3,1,4,2,5,1,6,2].
...
[1,2,3,1,2] is invalid because the substring [1,2] appears twice.
[1,2,1] is invalid because the substring [1,2] appears twice (once forward and once backward).
		

Links

• Peter Kagey, Haskell program for A282193.

Crossrefs

Cf. A282168 is the sum analog.

Cf. A081456, A282164, A282169, A282170.

Extensions

Terms a(13) onward from Max Alekseyev, Feb 05 2025