

A294448


Discrepancy of the Kolakoski sequence A000002.


2



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
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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.


REFERENCES

Richard P Brent, Fast algorithms for the Kolakoski sequence, Slides from a talk, 2016; https://mathspeople.anu.edu.au/~brent/pd/KolakoskiUNSW.pdf


LINKS

Table of n, a(n) for n=1..90.


CROSSREFS

Cf. A000002, A088568.
For records see A294449.
Sequence in context: A080732 A301295 A215036 * A088568 A317161 A123737
Adjacent sequences: A294445 A294446 A294447 * A294449 A294450 A294451


KEYWORD

sign


AUTHOR

N. J. A. Sloane, Nov 21 2017


STATUS

approved



