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

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Example

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.

Sequence in context: A244954 A353830 A060374 * A085961 A175325 A223525

Adjacent sequences: A074293 A074294 A074295 * A074297 A074298 A074299

Keyword

nonn

Author

Jon Perry, Sep 21 2002

Extensions

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

More terms from Sean A. Irvine, Jan 18 2025

Status

approved