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A272729 a(n) is the number of repetitions of 2n-1 in A272727. 4
1, 2, 1, 3, 2, 1, 1, 4, 1, 3, 2, 2, 1, 1, 1, 5, 2, 1, 1, 4, 1, 3, 1, 3, 2, 2, 2, 1, 1, 1, 1, 6, 1, 3, 2, 2, 1, 1, 1, 5, 2, 1, 1, 4, 2, 1, 1, 4, 1, 3, 1, 3, 1, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 7, 2, 1, 1, 4, 1, 3, 1, 3, 2, 2, 2, 1, 1, 1, 1, 6, 1, 3, 2, 2, 1, 1, 1, 5, 1, 3, 2, 2, 1, 1, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, value of A272728 at the n-th local maximum.

Also, the trajectory of 1 under the morphism n->[1,1..1,n+1] (the number of 1's is n-1).

Average value tends to 2.

Number n makes its first appearance at the position 2^(n-1) and has frequency 1/2^n.

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..8192

Index entries for sequences that are fixed points of mappings

EXAMPLE

The morphism acts as follows:

1->2; 2->1,3; 3->1,1,4; 4->1,1,1,5; etc.

The trajectory starts as:

1 ->

2 ->

1,3 ->

2,1,1,4 ->

1,3,2,2,1,1,1,5 -> ...

The result of k iterations is a series with 2^(k-1) terms; their sum is 2^k.

If A001511 is laid out in a similar irregular triangle, each row

would contain the same terms, albeit in a different order:

1,

2,

1,3,

1,2,1,4,

1,2,1,3,1,2,1,5...

MATHEMATICA

Flatten@NestList[Flatten[Append[ConstantArray[1, # - 1], # + 1] & /@ #] &, {1}, 7]

CROSSREFS

Cf. A001511, A272727, A272728.

Sequence in context: A165011 A213883 A192190 * A064034 A231635 A266640

Adjacent sequences:  A272726 A272727 A272728 * A272730 A272731 A272732

KEYWORD

nonn

AUTHOR

Ivan Neretin, May 05 2016

STATUS

approved

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Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)