A282167 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, and no self-adjacent terms.

1, 3, 6, 7, 11, 13, 17, 19, 25, 27, 31, 35, 39, 45, 47, 53, 57, 63, 67, 73, 77, 83, 87, 95, 99, 105, 111, 117, 123, 129, 135, 141, 149, 153, 161, 167, 175, 181, 189, 195, 203, 209, 217, 223, 231, 237, 247, 253, 261, 269, 277, 285, 293, 301, 309, 317, 325, 333, 341, 351, 357, 367, 375, 385, 393, 403, 411, 421, 429, 439

Offset: 1

Author

Peter Kagey, Feb 07 2017

Keywords

• nonn

Comments

For n>=7, we seem to have a(n) = a(n-1) + a(n-2) - a(n-3) + d(n), where d(n) is in {-2, 0, 2}. Compare to A282166. - Max Alekseyev, Jun 13 2025

Examples

			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).
  a(1)  = 1  via [1];
  a(2)  = 3  via [1,2];
  a(3)  = 6  via [1,2,3];
  a(4)  = 7  via [1,2,3,1];
  a(5)  = 11 via [1,2,3,1,4];
  a(6)  = 13 via [1,2,3,1,4,2];
  a(7)  = 17 via [1,2,3,1,4,5,1];
  a(8)  = 19 via [1,2,3,1,4,2,5,1];
  a(9)  = 25 via [1,2,3,1,4,2,5,1,6];
  a(10) = 27 via [1,2,3,1,4,2,5,1,6,2].
		

Crossrefs

Cf. A259280, A282166, A282168.

Extensions

Terms a(11) onward from Max Alekseyev, Feb 05 2025