A294448 Discrepancy of the Kolakoski sequence A000002.

-1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, -2, -1, -2, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2

Offset

1,12

Comments

The discrepancy is defined by a(n) = Sum_{i=1..n} (-1)^k(i), where k(i) = A000002(i). The negative of this sequence is already in the OEIS (A088568), but does not seem to be found if one looks up -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, ..., so this version has been added for completeness.

See A088568 for more information and references.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Richard P. Brent, Fast algorithms for the Kolakoski sequence, Slides from a talk, 2016.

Crossrefs

Cf. A000002, A088568.

For records see A294449.

Sequence in context: A080732 A301295 A215036 * A088568 A317161 A307198

Adjacent sequences: A294445 A294446 A294447 * A294449 A294450 A294451

Keyword

sign,look

Author

N. J. A. Sloane, Nov 21 2017

Status

approved