cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A283557 The number of positive integer sequences of length n with no duplicate substrings of length greater than 1 and a minimal product (= A282164(n)).

Original entry on oeis.org

1, 1, 3, 2, 2, 6, 6, 24, 24, 120, 120, 1200, 1440, 4320, 4320, 8640, 30240, 60480, 483840, 967680, 1935360, 3870720, 17418240, 34836480, 348364800, 696729600, 1741824000, 3483648000, 19160064000, 38320128000, 689762304000, 1379524608000, 9656672256000, 16554295296000, 66217181184000
Offset: 1

Views

Author

Peter Kagey, Mar 10 2017

Keywords

Comments

Surprisingly, a(n) = A282164(n) for n in { 1, 2, 4, 6, 8, 10, 13, 14, 19, 25, 32, 34, 35, ... }. - Max Alekseyev, Feb 06 2025

Examples

			For n = 7, the a(7) = 6 sequences are
1,3,1,2,2,1,1;
1,2,2,1,3,1,1;
1,3,1,1,2,2,1;
1,1,3,1,2,2,1;
1,2,2,1,1,3,1; and
1,1,2,2,1,3,1.

Links

Crossrefs

A283558 is the sum analog.
Cf. A282164, A284434, A284435, A284436.

Extensions

Terms a(11) onward from Max Alekseyev, Feb 06 2025

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.

Original entry on oeis.org

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

Views

Author

Peter Kagey, Feb 08 2017

Keywords

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

Crossrefs

Cf. A282168 is the sum analog.
Cf. A081456, A282164, A282169, A282170.

Extensions

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

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.

Original entry on oeis.org

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

Views

Author

Peter Kagey, Feb 07 2017

Keywords

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

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.

Original entry on oeis.org

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

Views

Author

Peter Kagey, Feb 07 2017

Keywords

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
Showing 1-4 of 4 results.

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