A074296 First occurrence of the smallest value subsequence of length n in the Kolakoski sequence (A000002).

1, 4, 3, 4, 13, 12, 28, 10, 9, 13, 13, 12, 13, 112, 20, 10, 13, 12, 13, 13, 12, 13, 112, 111, 10, 109, 108, 167, 4, 112, 4, 94, 20, 101, 91, 167, 13, 94, 13, 13, 94, 93, 1511, 91, 90, 157, 743, 94, 750, 776, 775, 217, 743, 742, 743, 743, 742, 173, 217, 216

Offset: 1

Author

Jon Perry, Sep 21 2002

Keywords

• nonn

Comments

The sequence of minimal sums begins 1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 15, 17, 18, 19, 21, ...

Examples

			a(3) = 3 because the Kolakoski sequence starting at position 3 is 2, 1, 1, which sums to 4, which is the smallest possible sum of 3 consecutive terms.
a(8) = 10 because the Kolakoski sequence starting at position 10 is 1, 2, 2, 1, 1, 2, 1, 1, which sums to 11, which is the smallest possible sum of 8 consecutive values in the Kolakoski sequence. Note that we cannot find a sequence of length eight with a sum of 10 because it would have to be of the form 1, 1, 2, 1, 1, 2, 1, 1, which would mean that 2, 1, 2, 1, 2 would have to appear earlier in the sequence, which would mean that 1, 1, 1 would have to appear even earlier in the sequence, which is impossible.
		

Crossrefs

Cf. A000002, A074297, A074298.

Extensions

a(8)-a(15) from and edited by Nathaniel Johnston, May 02 2011

More terms from Sean A. Irvine, Jan 18 2025