A282169 a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings of length greater than 1, and every number different from its neighbors.

1, 2, 2, 6, 6, 24, 24, 120, 120, 576, 720, 2880, 4320, 17280, 30240, 120960, 241920, 967680, 1935360, 8709120, 17418240, 87091200, 174182400, 870912000, 1741824000, 9580032000, 19160064000, 104509440000, 229920768000, 1149603840000, 2759049216000, 13795246080000, 33108590592000, 165542952960000, 430411677696000

Offset: 1

Author

Peter Kagey, Feb 07 2017

Keywords

• nonn

Examples

			[1,1] is not a valid sequence because 1 is self-adjacent.
[1,2,3,1,2] is not valid because the substring [1,2] appears twice.
  a(1)  = 1   via [1];
  a(2)  = 2   via [1,2];
  a(3)  = 2   via [1,2,1];
  a(4)  = 6   via [1,2,1,3];
  a(5)  = 6   via [1,2,1,3,1];
  a(6)  = 24  via [1,2,1,3,1,4];
  a(7)  = 24  via [1,2,1,3,1,4,1];
  a(8)  = 120 via [1,2,1,3,1,4,1,5];
  a(9)  = 120 via [1,2,1,3,1,4,1,5,1];
  a(10) = 576 via [1,2,1,3,1,4,2,3,4,1];
  a(11) = 720 via [1,2,1,3,1,4,1,5,1,6,1].
		

Crossrefs

Cf. A081456, A282164, A282193, A282170, A284434.

Cf. A282166 is the sum analog.

Extensions

Terms a(12) onward from Max Alekseyev, Feb 04 2025