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A294448
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Discrepancy of the Kolakoski sequence A000002.
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4
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-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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,12
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COMMENTS
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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.
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LINKS
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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.
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CROSSREFS
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Cf. A000002, A088568.
For records see A294449.
Sequence in context: A080732 A301295 A215036 * A088568 A317161 A307198
Adjacent sequences: A294445 A294446 A294447 * A294449 A294450 A294451
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KEYWORD
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sign,look
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AUTHOR
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N. J. A. Sloane, Nov 21 2017
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STATUS
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approved
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