A234322 Percentage of 1's among the first n terms of the Kolakoski sequence A000002.

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

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), 681-682.

J. Malkevitch, Periods, AMS Feature Column, Jan 2014.

R. Oldenburger, Exponent trajectories in symbolic dynamics, Trans. Amer. Math. Soc., 46 (1939), 453-466.

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