

A234322


Percentage of 1's among the first n terms of the Kolakoski sequence A000002.


3



100, 50, 33, 50, 60, 50, 57, 50, 44, 50, 45, 42, 46, 50, 47, 50, 53, 50, 47, 50, 48, 50, 52, 50, 52, 50, 48, 50, 52, 50, 52, 53, 52, 53, 51, 50, 51, 50, 49, 50, 51, 50, 51, 50, 49, 50, 49, 50, 51, 50, 51, 52, 51, 50, 51, 50, 49, 50, 51, 50, 51, 50, 49, 50, 49, 48, 49, 50, 49, 50, 51, 50
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OFFSET

1,1


COMMENTS

Percentage of 1's (rounded) among the first n terms of A000002.
See A000002 for additional comments, references, links, formulas, examples, programs, and crossrefs.
It is conjectured that a(n) = 50 for all n sufficiently large.
Among the first 1500000 terms of the sequence, a(n) = 51 appears last at a(295) and a(n) = 49 appears last at a(471).  Paolo Bonzini, Jul 06 2016


LINKS

Paolo Bonzini, Table of n, a(n) for n = 1..500
W. Kolakoski and N. Ucoluk, Problem 5304: Self Generating Runs, Amer. Math. Monthly, 72 (1965), 674; 73 (1966), 681682.
J. Malkevitch, Periods, AMS Feature Column, Jan 2014.
R. Oldenburger, Exponent trajectories in symbolic dynamics, Trans. Amer. Math. Soc., 46 (1939), 453466.


FORMULA

a(n) = nearest integer to 100*A156077(n)/n.


EXAMPLE

There are five 1's among the first twelve terms of A000002 = 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, ..., so a(12) = nearest integer to 100*5/12 = 41.666... rounded = 42.


CROSSREFS

Cf. A000002, A156077.
Sequence in context: A153674 A008903 A033420 * A260707 A180102 A242615
Adjacent sequences: A234319 A234320 A234321 * A234323 A234324 A234325


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Jan 03 2014


STATUS

approved



