A157196 - OEIS

A157196

a(n) = (1/2)*(sum of elements of n-th run) using 1 and 2 starting with 1,1.

1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1

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OFFSET

1,3

COMMENTS

We conjecture that the density of 1's in the sequence approaches 2/3 as n -> infinity. This conjecture is proved in the paper of Shallit.

LINKS

Table of n, a(n) for n=1..105.

Daniel Hoyt, Visual representation of the sequence in the style of the Kolakoski sequence.

Daniel Hoyt, Representing the sequence visually.

Jeffrey Shallit, Cloitre's Self-Generating Sequence, arXiv:2501.00784 [math.CO], 2025.

EXAMPLE

Write the sums of elements in each run, you obtain: 2,2,4,2,2,2,2,4,2,2,4,2,2,4,4,... dividing by 2 you get: 1,1,2,1,1,1,1,2,1,1,2,1,1,2,2,... the sequence itself.

MAPLE

mx:= 1000: l:= [1$2]: a:= n-> l[n]:

for h from 2 while nops(l)<mx do

t:= 2-irem(h, 2); l:= [l[], t$(l[h]*2/t)]

od:

seq (a(n), n=1..120); # Alois P. Heinz, May 31 2012

CROSSREFS

Cf. A000002, A157129, A336810.

Sequence in context: A372331 A318498 A093997 * A300410 A362845 A293451

Adjacent sequences: A157193 A157194 A157195 * A157197 A157198 A157199

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 24 2009

EXTENSIONS

More terms from Alvin Hoover Belt, May 31 2012

STATUS

approved

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