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

1,2

Links

Table of n, a(n) for n=1..32.

Example

  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.

Sequence in context: A325803 A130865 A327630 * A105725 A005226 A087310

Adjacent sequences: A282167 A282168 A282169 * A282171 A282172 A282173

Keyword

nonn

Author

Peter Kagey, Feb 07 2017

Extensions

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

Status

approved