

A272729


a(n) is the number of repetitions of 2n1 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
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OFFSET

1,2


COMMENTS

Also, value of A272728 at the nth local maximum.
Also, the trajectory of 1 under the morphism n>[1,1..1,n+1] (the number of 1's is n1).
Average value tends to 2.
Number n makes its first appearance at the position 2^(n1) 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^(k1) 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



