A282168 a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings (forward or backward) of length greater than 1.

1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 29

Offset

1,2

Comments

Examples:

[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).

This sequence is distinct from A025224: a(28) = 102 > A025224(28).

Other known terms:

a(19) = 57;

a(28) = 102;

a(40) = 174;

a(53) = 265.

Links

Table of n, a(n) for n=1..12.

Example

  a(1)  = 1   via [1];
  a(2)  = 2   via [1,1];
  a(3)  = 4   via [1,1,2];
  a(4)  = 6   via [1,1,2,2];
  a(5)  = 8   via [1,1,2,3,1];
  a(6)  = 10  via [1,1,2,2,3,1];
  a(7)  = 13  via [1,1,2,2,3,3,1];
  a(8)  = 16  via [1,1,2,2,3,1,4,2];
  a(9)  = 19  via [1,1,2,2,3,3,1,4,2];
  a(10) = 22  via [1,1,2,2,3,1,4,2,5,1];
  a(11) = 25  via [1,1,2,2,3,3,1,4,2,5,1];
  a(12) = 29  via [1,1,2,2,3,3,1,4,4,2,5,1].

Crossrefs

Cf. A259280, A282166, A282167.

Sequence in context: A061168 A130798 A165453 * A025224 A294023 A096182

Adjacent sequences: A282165 A282166 A282167 * A282169 A282170 A282171

Keyword

nonn,more

Author

Peter Kagey, Feb 07 2017

Status

approved