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

1,3

Links

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

Peter Kagey, Haskell program for A282193.

Example

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).

Crossrefs

Cf. A282168 is the sum analog.

Cf. A081456, A282164, A282169, A282170.

Sequence in context: A283021 A309039 A087902 * A180213 A081457 A261206

Adjacent sequences: A282190 A282191 A282192 * A282194 A282195 A282196

Keyword

nonn

Author

Peter Kagey, Feb 08 2017

Extensions

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

Status

approved