A282168 - OEIS

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

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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

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

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Feb 07 2017

STATUS

approved