A282170 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, and no self-adjacent terms.

1, 2, 6, 6, 24, 48, 120, 240, 1440, 2880, 10080, 20160, 120960, 322560, 1209600, 2903040, 17418240, 58060800, 174182400, 638668800, 3483648000, 15328051200, 38320128000, 199264665600, 919683072000, 4828336128000, 11955879936000, 71735279616000, 334764638208000, 1506440871936000, 5021469573120000, 30128817438720000

Offset: 1

Author

Peter Kagey, Feb 07 2017

Keywords

• nonn

Examples

			  a(1)  = 1     via [1];
  a(2)  = 2     via [1,2];
  a(3)  = 6     via [1,2,3];
  a(4)  = 6     via [1,2,3,1];
  a(5)  = 24    via [1,2,3,1,4];
  a(6)  = 48    via [1,2,3,1,4,2];
  a(7)  = 120   via [1,2,3,1,4,5,1];
  a(8)  = 240   via [1,2,3,1,4,2,5,1];
  a(9)  = 1440  via [1,2,3,1,4,2,5,1,6];
  a(10) = 2880  via [1,2,3,1,4,2,5,1,6,2];
  a(11) = 10080 via [1,2,3,1,4,2,5,1,6,7,1].
Examples:
  [1,1] is invalid because 1 is self-adjacent.
  [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).
		

Crossrefs

Cf. A081456, A282164, A282169, A282170, A282193.

Cf. A282167 is the sum analog.

Extensions

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